LOGARITHMIC  AND 
TRIGONOMETRIC  TABLES 


A  SERIES  OF  MATHEMATICAL  TEXTS 
(FOR  COLLEGES) 

EDITED    BY 

EARLE  RAYMOND  HEDRICK 


THE   CALCULUS 

BY  ELLEBY  WILLIAMS  DAVIS  and  WILLIAM  CHARLES  BRENKE. 

ANALYTIC   GEOMETRY  AND  ALGEBRA 

BY  ALEXANDER  ZIWET  and  Louis  ALLEN  HOPKINS. 

ELEMENTS   OF  ANALYTIC   GEOMETRY 

BY  ALEXANDER  ZIWET  and  Louis  ALLEN  HOPKINS. 

PLANE  AND   SPHERICAL   TRIGONOMETRY 
BY  ALFRED  MONROE  KENYON  and  Louis  INGOLD. 

ELEMENTARY   MATHEMATICAL  ANALYSIS 

BY  JOHN  WESLEY  YOUNG  and  FRANK  MILLETT  MORGAN. 

PLANE   TRIGONOMETRY 

BY  JOHN  WESLEY  YOUNG  and  FRANK  MILLETT  MORGAN. 

COLLEGE  ALGEBRA 

BY  ERNEST  BROWN  SKINNER. 

MATHEMATICS   FOR   AGRICULTURE   AND   GENERAL 

SCIENCE 
BY  ALFRED  MONROE  KENYON  and  WILLIAM  VERNON  LOVTTT. 

MATHEMATICS   FOR   STUDENTS   OF  AGRICULTURE 
BY  SAMUEL  EUGENE  RASOR. 

THE   MACMILLAN   TABLES 

Prepared  under  the  direction  of  EARLE  RAYMOND  HEDBICK. 

A  BRIEF  COURSE   IN   COLLEGE  ALGEBRA 
BY  WALTER  BURTON  FORD. 

COLLEGE  ALGEBRA 

BY  ARTHUR  M.  HARDING  and  GEORGE  W.  MULLINS. 

PLANE   TRIGONOMETRY 

BY  ARTHUR  M.  HARDING  and  GEORGE  W.  MULLINS. 

GENERAL   MATHEMATICS 

BY  CLINTON  H.  CURRIER  and  EMERY  E.  WATSON. 

PROJECTIVE   PURE   GEOMETRY 
BY  THOMAS  F.  HOLGATE 

ANALYTIC   GEOMETRY 

BY  ARTHUR  M.  HARDING  and  GEORGE  W.  MULLINS. 

INTRODUCTION   TO   HIGHER  GEOMETRY 
BY  WILLIAM  C.  GRAUSTEIN. 

INTRODUCTION  TO  TRIGONOMETRY  AND  ANALYTIC 

GEOMETRY 
BY  ERNEST  BROWN  SKINNER. 

DIFFERENTIAL  AND  INTEGRAL  CALCULUS 

BY  JOHN  HAVEN  NEELLEY  and  JOSHUA  IRVING  TRACEY. 

THE  MONGEAN  METHOD  OF  DESCRIPTIVE  GEOME- 
TRY 
BY  WILLIAM  HENRY  ROEVER. 

DIFFERENTIAL  EQUATIONS 
BY  NELSON  B.  CONKWRIGHT. 

TABLES  OF  INTEGRALS  AND  OTHER  MATHEMATICAL 

DATA 
BY  HERBERT  BRISTOL  DWIGHT. 

AN  INTRODUCTION  TO  THE  MATHEMATICS  OF  LIFE 

INSURANCE 
BY  WALTER  O.  MENGE  and  JAMES  W.  GLOVER. 


LOGAEITHMIC  AND 
TRIGONOMETRIC  TABLES 


REVISED  EDITION 


PREPARED  UNDER  THE  DIRECTION  OF 
EARLE  RAYMOND  HEDRICK 


ENTIRELY  RE-SET  IN  A  NEW  TYPE  FACE 


NEW  YORK 

THE  MACMILLAN  COMPANY 


COPYRIGHT,  1913  AND  1920, 
Br  THE  MACMILLAN  COMPANY. 


All  rights  reserved — no  part  of  this  book 
may  be  reproduced  in  any  form  without 
permission  in  writing  from  the  publisher, 
except  by  a  reviewer  who  wishes  to  quote 
brief  passages  in  connection  with  a  review 
written  for  inclusion  in  magazine  or 
newspaper. 


Set  up  and  electrotyped.  Revised  edition  published  August,  1920.  Reprinted 
April,  1924 ;  May,  September,  December,  1925 ;  April,  June,  1926 ;  January, 
July,  1927  ;  March,  December,  1928 ;  November,  1929  ;  October,  November,  1930 ; 
April,  October,  1931;  February,  3932;  April,  1933;  May,  1933;  November,  1933; 
July,  1935;  May,  1936;  December,  1937;  May,  1938;  June,  1938;  December,  1939; 
August,  1940;  October,  1940;  May,  1941. 


Printed  in  the  United  States  of  America 


PREFACE 

The  present  edition  of  this  book  contains  all  of  the  tables  in  the 
previous  editions.  All  have  been  reset  in  a  new  and  very  readable  type. 

Great  care  has  been  exercised  to  preserve  and  to  increase  the  great 
degree  of  reliability  that  existed  in  the  previous  edition.  For  careful 
reading  of  the  proofs,  I  am  indebted  to  my  daughter  Elisabeth  and 
her  husband,  Mr.  Richard  L.  Miller,  to  several  of  my  own  students, 
and  to  the  following  friends  in  other  institutions,  sometimes  with  the 
aid  of  their  students :  Professor  C.  H.  Currier,  Brown  University ;  Pro- 
fessor H.  T.  Davis,  University  of  Indiana;  Professor  H.  B.  Dwight, 
Massachusetts  Institute  of  Technology;  Professor  W.  B.  Ford,  Uni- 
versity of  Michigan ;  Professor  A.  M.  Harding,  University  of  Arkansas  ; 
Professor  C.  G.  Jaeger,  Pomona  College ;  Professors  H.  W.  Kuhn  and 
J.  H.  Weaver,  Ohio  State  University;  Professor  L.  S.  Johnston,  Uni- 
versity of  Detroit;  Professors  A.  J.  Kempner  and  C.  A.  Hutchinson, 
University  of  Colorado;  Professor  G.  W.  Mullins,  Barnard  College 
(Columbia  University) ;  Professor  L.  M.  Passano,  Massachusetts  Insti- 
tute of  Technology;  Professors  H.  L.  Rietz,  Roscoe  Woods,  and  J.  F. 
Reilly,  University  of  Iowa;  Professor  E.  E.  Watson,  Iowa  State  Teachers 
College  at  Cedar  Falls;  Dr.  E.  W.  Wilson,  Cambridge,  Mass.;  and  Pro- 
fessor Kathryn  Wyant,  Athens  College,  Athens,  Alabama.  Each  of 
these  persons  or  groups  has  read  the  complete  proof.  With  deep  feeling, 
I  may  record  also  that  the  late  Professor  Louis  Ingold  of  the  University 
of  Missouri  read  the  proofs  up  to  page  54,  and  had  sent  me  the  last  of 
these  pages  within  a  week  of  his  sudden  death  on  January  25,  1935. 

These  careful  readings  render  the  possibility  of  printers'  errors  ex- 
tremely remote.  While  the  calculation  of  the  probability  that  an 
undiscovered  error  exists  is  not  simple,  a  strict  account  has  been  kept  of 
each  error  found  and  of  the  total  number  not  found  by  any  one  group  of 
readers,  so  that  a  basis  for  a  statistical  calculation  is  known:  the  result- 
ing probability  that  even  one  undiscovered  printers'  error  exists  is  not 
more  than  one  in  many  thousands. 

I  desire  to  express  here  my  thanks  to  all  those,  particularly  those 
mentioned  above,  who  have  assisted  in  the  effort  to  make  these  tables 
so  free  from  errors  and  therefore  so  reliable.  I  know  of  no  comparable 
method  for  securing  this  quality  in  a  set  of  tables. 

I  repeat  also  my  acknowledgment  made  in  the  original  edition  to 
many  previously  existing  tables,  particularly  those  of  Vega  and  those 
of  Hoiiel.  During  the  proof-reading,  those  who  have  assisted  have 
compared  these  tables  with  a  great  variety  of  existing  tables,  including 
several  high-place  tables,  and  the  values  have  been  recalculated  and 
checked  whenever  a  disagreement  has  been  discovered. 

Finally,  I  wish  to  mention  the  excellent  cooperation  of  the  editorial 
staff  of  the  Macmillan  Company  under  the  able  direction  of  Mr.  F.  T. 
Sutphen. 

E.  R.  HEDRICK 


CONTENTS 

PAGES 

EXPLANATION  OF  THE  TABLES vii-xvi 

TABLES  PRINCIPALLY  TO  FIVE  PLACES 

TABLE  I.  COMMON  LOGARITHMS  OP  NUMBERS  ....  1-19 
TABLE  la.  CONDENSED  LOGARITHMS  AND  ANTILOGARITHMS  .  .  20 
TABLE  II.  ACTUAL  VALUES  OP  THE  TRIGONOMETRIC  FUNCTIONS.  21-44 
TABLE  Ilia.  VAIUES  OP  S  AND  T  FOR  INTERPOLATION  ...  45 
TABLE  III.  COMMON  LOGARITHMS  OF  THE  TRIGONOMETRIC  FUNC- 
TIONS    45-90 

REDUCTION  OP  DEGREES  TO  RADIANS  ....  91 

TRIGONOMETRIC  FUNCTIONS  OF  ANGLES  IN  RADIAN'S  .  92-93 

REDUCTION  OF  RADIANS  TO  DEGREES  ....  93 

POWERS — ROOTS — RECIPROCALS 94-111 

NAPIERIAN  OR  NATURAL  LOGARITHMS  ....  112-114 

MULTIPLES  OF  M  AND  OF  1/M 115 

VALUES  AND  LOGARITHMS  OF  HYPERBOLIC  FUNCTIONS  116-122 

VALUES  AND  LOGARITHMS  OF  HAVERSINES  .       .       .  123-125 

FACTOR  TABLE — LOGARITHMS  OF  PRIMES    .       .       .  126-127 

COMPOUND  INTEREST 128 

COMPOUND  DISCOUNT 129 

AMOUNT  OF  AN"  ANNUITY 130 

PRESENT  VALUE  OF  AN  ANNUITY 131 

LOGARITHMS  FOR  INTEREST  COMPUTATIONS  .       .       .  132 

AMERICAN  EXPERIENCE  MORTALITY  TABLE  .       .       .  132 

IMPORTANT  CONSTANTS    .  133 


IV. 

V. 

Va. 
VI. 


TABLE 
TABLE 
TABLE 
TABLE 
TABLE    VII. 
TABLE  VIII. 
TABLE     IX. 
TABLE      X. 
TABLE     XL 
TABLE    Xlla. 
TABLE   XII6. 
TABLE   XIIc. 
TABLE    Xlld. 
TABLE   Xlle. 
TABLE   XII/. 
TABLE  XIII. 


BRIEF  TABLES— PRINCIPALLY  TO  FOUR  PLACES 

TABLE  XlVa.  COMMON  LOGARITHMS 134-135 

TABLE  XlVb.  ANTILOGARITHMS 136-137 

TABLE  XIVc.  VALUES  AND  LOGARITHMS  OF  TRIGONOMETRIC  FUNC- 
TIONS .   138-142 


EXPLANATION  OF  THE  TABLES 

TABLE  I.    FIVE-PLACE  COMMON  LOGARITHMS  OF 
NUMBERS  FROM   1  TO  10000 

1.  Common  Logarithms.    The  power  to  which  10  must  be  raised  to  produce 
any  number  n  is  called  the  common  logarithm  *  of  n.     Thus  log  10  =  1, 
log  100  =  2,  log  1000  =  3,  etc.;  log  1  =  0,  log  0.1  =  -1;  log  0.01  =  -2, 
log  0.001  =  —  3,  etc.     In  general,  if  10*  =  n,  I  is  called  the  common  logarithm 
of  n,  and  is  denoted  by  log  n. 

2.  Fundamental  Principles.     Logarithms  constitute  a  great  labor-saving  de- 
vice in  arithmetical  computations.     The  principles  of  their  application  are 
stated  as  follows: 

I.  The  logarithm  of  a  -product  is  equal  to  the  sum  of  the  logarithms  of  the  factors: 
log  ab  =  log  a  +  log  6.     This  follows  from  the  fact  that  if  10'  =  a  and  itf1  =  6, 
IQI+L  =  a- b.     In  brief:  to  multiply,  add  logarithms. 

II.  The  logarithm  of  a  fraction  is  equal  to  the  difference  obtained  by  subtracting 
the  logarithm  of  the  denominator  from  the  logarithm  of  the  numerator:  log  (afb) 
=  log  a  -  log  6.     For,  if  10'  =  a  and  10L  =  6,  then  10'-^  =  0-7-6.     In  brief: 
to  divide,  subtract  logarithms. 

III.  The  logarithm  of  a  power  is  equal  to  the  logarithm  of  the  base  multiplied 
by  the  exponent  of  the  power:  log  a6  =  b  log  a.     This  follows  from  the  fact  that 
if  10'  =  a,  then  10'6  =  ab. 

IV.  The  logarithm  of  a  root  of  a  number  is  found  by  dividing  the  logarithm  of 
the  number  by  the  index  of  the  root:  log  ^a  =  (log  a)/6.     This  follows  from  the 
fact  that  if  10'  =  a,  then  10"6  =  a1/6  =  \Ja. 

Corollary  of  II.     The  logarithm  of  the  reciprocal  of  a  number  is  the  negative 
of  the  logarithm  of  the  number:  log  (I/a)  =  —log  a,  since  log  1  =  0. 

3.  Characteristic  and  Mantissa.    Every  real  positive  number  has  a  real 
common  logarithm.     If  a  and  b  are  any  two  real  positive  numbers  such  that 
a  <b,  then  log  a  <  log  6.     Neither  zero  nor  any  negative  number  has  a  real 
logarithm. 


a 

1 

10 

100 

1000 

10000 

100000 

1000000 

10000000 

log  a 

0 

1 

2 

3 

4 

5 

6 

7 

Inspection  of  the  preceding  table  shows  that 

the  logarithm  of  every  number  between  1  and  10  is  a  proper  fraction, 
the  logarithm  of  every  number  between  10  and  100  is  1  +  a  fraction, 
the  logarithm  of  every  number  between  100  and  1000  is  2  +  a  fraction; 


*  Common  logarithms  are  exponents  of  the  base  10;  other  systems  of  logarithms  have  bases 
different  from  10;  Napierian  logarithms  (see  Table  VII,  p.  112)  have  a  base  denoted  by  e,  an 
irrational  number  whose  value  is  approximately  2.71828.  When  it  is  necessary  to  call  attention 
to  the  base,  the  expression  logio  n  will  mean  common  logarithm  of  n;  log,,  n  will  mean  the 
Napierian  logarithm,  etc.;  but  in  this  book  log  n  denotes  Iog10  n  unless  otherwise  explicitly  stated. 


vm 


EXPLANATION  OF  THE  TABLES 


C§3 


and  so  on.  It  is  evident  that  the  logarithm  of  every  number  (not  an  exact 
power  of  10)  consists  of  a  whole  number  +  a  fraction  (usually  written  as  a 
decimal).  The  whole  number  is  called  the  characteristic;  the  decimal  is 
called  the  mantissa.  The  characteristic  of  the  logarithm  of  any  number 
greater  than  1  may  be  determined  as  follows: 

RULE  I.  The  characteristic  of  any  number  greater  than  1  is  one  less  than  the 
number  of  digits  before  the  decimal  point. 

The  following  table  shows  that 


a 

.0000001 

.000001 

.00001 

.0001 

.001 

.01 

.1 

1 

log  a 

-7 

-6 

-5 

-4 

-3 

-2 

-1 

0 

the  logarithm  of  every  number  between  0.1  and  1  is  —1  +  a  fraction, 

the  logarithm  of  every  number  between  0.01  and  0.1  is  --2  +  a  fraction, 

the  logarithm  of  every  number  between  0.001  and  0.01  is  —  3  +  a  fraction; 
and  so  on. 

Thus  the  characteristic  of  every  number  between  0  and  1  is  a  negative  whole 
number;  there  is  a  great  practical  advantage,  however,  in  computing,  to 
write  these  characteristics  as  follows:  —  1  =  9  —  10,  —  2  =  8  —  10,  —3 
=  7-10,  etc.  Thus,  the  logarithm  of  0.562  is  - 1  +  0.74974,  but  this  should 
be  written  9.74974  —  10;  and  similarly  for  all  numbers  less  than  1. 

RULE  II.  The  characteristic  of  a  nymber  less  than  1  is  found  by  subtracting 
from  9  the  number  of  ciphers  between  the  decimal  point  and  the  first  significant  digit, 
and  writing  —10  after  the  result. 

Thus,  the  characteristic  of  log  645  is  2  by  Rule  I;  the  characteristic  of 
log  64.5  is  1  by  (I);  of  log  6.45  is  0  by  (I);  of  log  0.645  is  9  -  10  by  (II);  of 
log  0.0645  is  8  -  10  by  (II). 

To  move  the  decimal  point  in  a  given  number  one  place  to  the  right  is  equiva- 
lent to  adding  one  unit  to  its  logarithm,  because  this  is  equivalent  to  multi- 
plying the  given  number  by  10.  Likewise,  to  move  the  decimal  point  one 
place  to  the  left  is  equivalent  to  subtracting  one  unit  from  the  logarithm. 
Hence,  moving  the  decimal  point  any  number  of  places  to  the  right  or  left 
does  not  change  the  mantissa  but  only  the  characteristic.* 

Thus,  5345,  5.345,  534.5,  0.05345,  534500  aU  have  the  same  mantissa. 

4.  Use  of  the  Table.  To  use  logarithms  in  computation  we  need  a  table 
arranged  so  as  to  enable  us  to  find,  with  as  little  effort  and  time  as  possible, 
the  logarithms  of  given  numbers  and,  vice  versa,  to  find  numbers  when  their 
logarithms  are  known.  Since  the  characteristics  may  be  found  by  means  of 
Rules  I  and  II,  p.  viii,  only  mantissas  are  given.  This  is  done  in  Table  I. 
Most  of  the  numbers  in  this  table  are  irrational,  and  must  be  represented  in 
the  decimal  system  by  approximations.  A  five-place  table  is  one  which  gives 
the  values  correct  to  five  places  of  decimals. 


*  Another  rule  for  finding  the  characteristic,  based  on  this  property,  is  often  useful:  if  the 
decimal  point  were  just  after  the  first  significant  figure,  the  characteristic  would  be  zero;  start 
at  this  point  and  count  the  digits  passed  over  to  the  left  or  right  to  the  actual  decimal  point; 
the  number  obtained  is  the  characteristic,  except  for  sign;  the  sign  is  negative  if  the  movement 
was  to  the  left,  positive  if  the  movement  was  to  the  right. 


§6]  COMMON  LOGARITHMS  ix 

PROBLEM  1.  To  find  the  logarithm  of  a  given  number.  First,  determine  the 
characteristic,  then  look  in  the  table  for  the  mantissa. 

To  find  the  mantissa  in  the  table  when  the  given  number  (neglecting  the 
decimal  point)  consists  of  four,  or  less,  digits  (exclusive  of  ciphers  at  the 
beginning  or  end),  look  in  the  column  marked  N  for  the  first  three  digits  and 
select  the  column  headed  by  the  fourth  digit:  the  mantissa  •will  be  found  at 
the  intersection  of  this  row  and  this  column.  Thus  to  find  the  logarithm  of 
72050,  observe  first  (Rule  I)  that  the  characteristic  is  4.  To  find  the  mantissa, 
fix  attention  on  the  digits  7205;  find  720  in  column  N,  and  opposite  it  in 
column  5  is  the  desired  mantissa,  0.85763;  hence  log  72050  =  4.85763.  The 
mantissa  of  0.07826  is  found  opposite  782  in  column  6  and  is  0.89354;  hence 
log  0.07826  =  8.89354  -  10. 

5.  Interpolation.     If  there  are  more  than  four  significant  figures  in  the 
given  number,  its  mantissa  is  not  printed  in  the  table;  but  it  can  be  found 
approximately  by  assuming  that  the  mantissa  varies  as  the  number  varies 
in  the  small  interval  not  tabulated;  while  this  assumption  is  not  strictly  cor- 
rect, it  is  sufficiently  accurate  for  use  with  this  table. 

Thus,  to  find  the  logarithm  of  72054  we  observe  that  log  72050  =  4.85763 
and  that  log  72060  =  4.85769.  Hence  a  change  of  10  in  the  number  causes 
a  change  of  0.00006  in  the  mantissa;  we  assume  therefore  that  a  change  of  4  in 
the  number  will  cause,  approximately,  a  change  of  0.4  X  0.00006  =  0.00002 
(dropping  the  sixth  place)  in  the  mantissa;  and  we  write  log  72054  =  4.85763 
+  0.00002  =  4.85765. 

The  difference  between  two  successive  values  printed  in  the  table  is  called 
a  tabular  difference  (0.00006,  above).  The  proportional  part  of  this  difference 
to  be  added  to  one  of  the  tabular  values  is  called  the  correction  (0.00002, 
above),  and  is  found  by  multiplying  the  tabular  difference  by  the  appropriate 
fraction  (0.4,  above).  These  proportional  parts  are  usually  written  without  the 
zeros,  and  are  printed  at  the  right-hand  side  of  each  page,  to  be  used  when 
mental  multiplications  seem  uncertain. 

Example  1.  Find  the  logarithm  of  0.0012647.  Opposite  126  in  column  4  find  0.10175; 
the  tabular  difference  is  34  (zeros  dropped) ;  0.7  X  34  is  given  in  the  margin  as  24;  this  correction 
added  gives  0.10199  as  the  mantissa  of  0.0012647;  hence  log  0.0012647  =  7.10199  —  10. 

Example  2.  Find  the  logarithm  of  1.85643.  Opposite  185  in  column  6  find  0.26858;  tabular 
difference  23;  0.43  X  23  is  given  in  the  margin  as  10;  this  correction  added  gives  0.26868  as  the 
mantissa  of  1.85643;  hence  log  1.85643  =  0.26868. 

6.  Reverse  Reading  of  the  Table.     PROBLEM  2.     To  find  the  number  when 
its  logarithm  is  known.*    First,  fixing  attention  on  the  mantissa  only,  find  from 
the  table  the  number  having  this  mantissa,  then  place  the  decimal  point  by 
means  of  the  two  following  rules:  t 

RULE  III.  //  the  characteristic  of  the  logarithm  is  positive  (in  which  case  the 
mantissa  is  not  followed  by  —Iff),  begin  at  the  left,  count  digits  one  more  than  the 
characteristic,  and  place  the  decimal  point  to  the  right  of  the  last  digit  counted. 


*  The  number  whose  logarithm  is  k  is  often  called  the  antilogarithm  of  k. 

t  Another  convenient  form  of  these  rules  is  as  follows:  if  the  characteristic  were  zero,  the 
decimal  point  would  fall  just  after  the  first  significant  figure;  move  the  decimal  point  one  place 
to  the  right  for  each  positive  unit  in  the  characteristic,  one  place  to  the  left  ior  each  negative 
unit  in  the  characteristic. 


X  EXPLANATION  OF  THE  TABLES  [§6 

RULE  IV.  //  the  characteristic  is  negative  (in  which  case  the  mantissa  will  be 
preceded  by  a  number  n  and  followed  by  —10),  prefix  9  —  n  ciphers,  and  place 
the  decimal  point  to  the  left  of  these  ciphers. 

Example  1.     Given  log  x  <=  1.22737,  to  find  z. 

Since  the  mantissa  is  22737,  we  look  for  22  in  the  first  column  and  to  the  right  and  below  for 
737,  which  we  find  in  column  8  opposite  168.  The  number  is  therefore  1688.  Since  the 
characteristic  is  +1,  we  begin  at  the  left,  count  2  places,  and  place  the  point;  hence  x  =  16.88. 

Example  2.     Given  log  x  =  2.24912,  to  find  x. 

This  mantissa  is  not  found  in  the  table;  in  such  cases  we  interpolate  as  follows:  select  the 
mantissa  in  the  table  next  less  than  the  given  mantissa,  and  write  down  the  corresponding 
number;  here,  1774;  the  tabular  difference  is  25;  the  actual  difference  (found  by  subtracting 
the  mantissa  of  1774  from  the  given  mantissa)  is  17;  hence  the  proportionality  factor  is  17/25 
=  0.68  or  0.7  (to  the  nearest  tenth).  Since  moving  the  decimal  point  does  not  affect  the  man- 
tissa, it  follows  that  the  digits  in  the  required  number  are  17747  (to  five  places).  The  charac- 
teristic 2  directs  to  count  3  places  from  the  left;  hence  x  =  177.47. 

RULE.  In  general,  when  the  given  mantissa  is  not  found  in  the  table,  write 
down  four  digits  of  the  number  corresponding  to  the  mantissa  in  the  table  next  less 
than  the  given  mantissa,  determine  a  fifth  figure  by  dividing  the  actual  difference 
by  the  tabular  difference,  and  locate  the  decimal  point  by  means  of  the  characteristic. 

7.  Cologarithms.     We  might  add  the  logarithms  of  the  factors  in  the  nu- 
merator and  from  this  sum  subtract  the  logarithm  of  the  denominator;  but  we 
can  shorten  the  operation  by  adding  the  negative  of  the  logarithm  of  the 
denominator  instead  of  subtracting  the  logarithm  itself.     The  negative  of  the 
logarithm  of  a  number  (when  written  in  convenient  form  for  computation) 
is  called  the  cologarithm  of  the  number.     We  may  find  the  negative  of  any 
number  by  subtracting  it  from  zero,  and  it  is  convenient  in  logarithmic  compu- 
tation to  write  zero  in  the  form  10.00000  —  10.     Thus  the  negative  of  2.17  is 
7.83  -  10;  the  negative  of  1.1432  -  10  is  8.8568.     Remembering  that  the 
cologarithm  of  a  number  is  its  negative  we  have  the  following  rule: 

To  find  the  cologarithm  of  a  number  begin  at  the  left  of  its  logarithm  (including 
the  characteristic)  and  subtract  each  digit  from  9,  except  the  last,*  which  subtract 
from  10;  if  the  logarithm  has  not  — 10  after  the  mantissa,  write  — 10  after  the  result; 
if  the  logarithm  has  —10  after  the  mantissa,  do  not  write  —10  after  the  result. 

By  this  rule  the  cologarithm  of  a  number  can  be  read  directly  out  of  the 
table  without  taking  the  trouble  to  write  down  the  logarithm.  Attention 
must  be  given  not  to  forget  the  characteristic.  The  use  of  the  cologarithm  is 
governed  by  the  principle: 

Adding  the  cologarithm  is  equivalent  to  subtracting  the  logarithm. 

la.     CONDENSED  LOGARITHMS  AND   ANTILOGARITHMS 

8.  Method  of  Computing  Logarithms.    This  table  is  a  rearrangement  of  the 
condensed  table  given  by  Hoiiel.f     From  it,  the  logarithm  of  any  number 
whatever  may  be  obtained  to  within  5  in  the  fifteenth  place;  or  to  any  desired 
degree  of  accuracy  less  than  this. 

To  illustrate  the  process,  we  shall  compute  log  TT  to  nine  places.  Taking 
T  =  3.14159  26535  8979,  we  divide  it  by  3,  the  first  significant  digit,  obtaining 

*  If  the  logarithm  ends  in  one  or  more  ciphers,  the  last  significant  digit  is  to  be  understood 
here. 

t  HottEL,  Recueil  de  Formules  et  de  Tables  numeriaues,  3d  ed.,  Paris,  Gauthier-Villars,  1901. 


§10]  TRIGONOMETRIC  FUNCTIONS  xi 

TT/S  =  1.04719  755  •  •  • .  We  then  divide  this  quotient  by  1.04,  etc.,  obtaining 
finally 

TT  =  3(1.04)  (1.006)  (1.0009)  (1.00001  5217223). 

We  can  obtain  the  logarithm  of  each  of  the  first  four  factors  from  this  table. 
The  logarithm  of  the  last  factor  can  be  obtained  by  multiplying  its  decimal 
part  by  M  =  0.43429  44819;  for  the  error  made  in  writing 

log  (1  +  z)  =  MX 

is  less  than  Mxz/2.  We  find  MX  either  by  using  the  fact  that  the  last  column 
in  this  table  gives  multiples  of  M,  or  (preferably)  by  Table  VIII,  page  115. 
Adding  the  five  logarithms  just  mentioned,  we  find 

log  TT  =  0.49714  98727  4, 

which  is  surely  correct  to  within  1  in  the  tenth  place.  The  correct  value  is 
0.4971498726  9  •••. 

The  process  may  be  applied  to  any  other  number  in  an  analogous  manner. 
Such  high-place  logarithms  are  occasionally  needed  in  statistical  work  and  in 
the  preparation  of  tables. 

9.  Method  of  Computing  Antilogarithms.     The  condensed  table  of  anti- 
logarithms  gives  eleven  significant  figures  (ten  decimal  places).     From  it, 
the  antilogarithm  of  any  number  can  be  computed  to  within  5  in  the  tenth 
significant  digit. 

Thus,  to  compute  the  antilogarithm  of  .4342944819  to  8  significant  figures, 
we  may  write 

1Q0.4M29  44819  _  noo-4)(100'03)(100-004)(100-0002)(100-00009)(100-0<)000  44819). 
The  first  five  factors  may  be  obtained  directly  from  the  table.     The  last  factor 
may  be  calculated  from  the  formula  10*  =  1  +  (l/3f)x.     The  error  in  this 
formula  is  less  than  3  in  the  (2fc)th  decimal  place  if  x  is  less  than  (0.1)*,  where 
k  >  1. 

However,  a  much  more  rapid  process  depends  on  the  use  of  Tables  I  and  XI 
with  this  table.  Thus,  by  Table  I,  100-*3429  =  2.718,  nearly.  By  Table  XI, 
log  2.718  =  0.43424  94524  •••.  Hence  10°-««9«819  =  (2.718) (10°-OOOM  5029S) 
=  (2.718) (100-00004)(10°-0000060298).  Obtaining  the  second  factor  from  this 
table,  and  the  last  factor  from  the  formula  10*  =  1  +  (l/Af)z,  by  Table  VIII, 
we  find  10°-«*2» 44819  =  2.71828  1828;  the  correct  value  is  2.718281828459  ••-. 
This  process  requires  only  two  long  multiplications. 

II.    FIVE-PLACE    TABLE    OF    THE    ACTUAL   VALUES   OF    THE 
TRIGONOMETRIC  FUNCTIONS  OF  ANGLES 

10.  Direct  Readings.    This  table  gives  the  sines,  cosines,  tangents,  and 
cotangents  of  the  angles  from  0°  to  45°;  and  by  a  simple  device,  indicated  by 
the  printing,  the  values  of  these  functions  for  angles  from  45°  to  90°  may  be 
read  directly  from  the  same  table.     For  angles  less  than  45°  read  down  the 
page,  the  degrees  being  found  at  the  top  and  the  minutes  on  the  left;  for  angles 
greater  than  45°  read  up  the  page,  the  degrees  being  found  at  the  bottom  and 
the  minutes  on  the  right. 

To  find  a  function  of  an  angle  (such  as  15°  27'.6,  for  example)  which  does 
not  reduce  to  an  integral  number  ot  minutes,  we  employ  the  process  of  inter- 


xii  EXPLANATION  OF  THE  TABLES  [§10 

polation.  To  illustrate,  let  us  find  tan  15°  27'.6.  In  the  table  we  find 
tan  15°  27'  =  0.27638  and  tan  15°  28'  =  0.27670;  we  know  that  tan  15°  27'.6 
lies  between  these  two  numbers.  The  process  of  interpolation  depends  on  the 
assumption  that  between  15°  27'  and  15°  28'  the  tangent  of  the  angle  varies 
directly  as  the  angle;  while  this  assumption  is  not  strictly  true,  it  gives  an 
approximation  sufficiently  accurate  for  a  five-place  table.  Thus  we  should 
assume  that  tan  15°  27'.5  is  halfway  between  0.27638  and  0.27670.  We  may 
state  the  problem  as  follows:  An  increase  of  1'  in  the  angle  increases  the  tangent 
0.00032;  assuming  that  the  tangent  varies  as  the  angle,  an  increase  of  0'.6  in  the 
angle  will  increase  the  tangent  by  0.6  X  0.00032  =  0.00019  (retaining  only 
five  places) ;  hence 

tan  15°  27'.6  =  0.27638  +  0.00019  =  0.27657. 

The  difference  between  two  successive  values  in  the  table  is  called,  as  in 
Table  I,  the  tabular  difference  (0.00032  above).  The  proportional  part  of  the 
tabular  difference  which  is  used  is  called  the  correction  (0.00019  above),  and 
is  found  by  multiplying  the  tabular  difference  by  the  appropriate  fraction  of 
the  smallest  unit  given  in  the  table. 

Example  1.     Find  sin  63°  52'. 8. 

We  find  sin  63°  52'  =  0.89777; 

tabular  difference  =  0.00013  (subtracted  mentally  from  the  table), 

correction  =  0.8  X  0.00013  =  0.00010  (to  be  added). 
Hence  sin  63°  52'.8  =  0.89787. 

Example  2.     Find  cos  654  24'.8. 

cos  65°  24'  =  0.41628; 
tabular  difference  =  26;  0.8  X  26  =21 

(to  be  subtracted  because  the  cosine  decreases  as  the  angle  increases). 
Hence  cos  65°  24'.8  =  0.41607. 

RULE.  To  find  a  trigonometric  function  of  an  angle  by  interpolation:  select 
the  angle  in  the  table  which  is  next  smaller  than  the  given  angle,  and  read  its  sine 
(cosine  or  tangent  or  cotangent  as  the  case  may  be)  and  the  tabular  difference. 
Compute  the  correction  as  the  proper  proportional  part  of  the  tabular  difference. 
In  case  of  sines  or  tangents  add  the  correction;  in  case  of  cosines  or  cotangents, 
subtract  it. 

11.  Reverse  Readings.  Interpolation  is  also  used  in  finding  the  angle  when 
one  of  its  functions  is  given. 

Example  1.     Given  sin  x  —  0.32845,  to  find  x. 

Looking  in  the  table  we  find  the  sine  which  is  next  less  than  the  given  sine  to  be  .32832, 
and  this  belongs  to  19°  10'.  Subtract  the  value  of  the  sine  selected  from  the  given  sine  to  obtain 
the  actual  difference  =  0.00013;  note  that  the  tabular  difference  =  0.00027.  The  actual  dif- 
ference divided  by  the  tabular  difference  gives  the  correction  =  13/27  =  0.5  as  the  decimal  of  a 
minute  (to  be  added).  Hence  x  =  19°  10'. 5. 

Example  2.     Given  cos  x  =  0.28432,  to  find  x. 

The  cosine  in  the  table  next  less  than  this  is  0.28429  and  belongs  to  73°  29';  the  tabular  dif- 
ference is  28;  the  actual  difference  is  3;  correction  =  3/28  =0.1  (to  be  subtracted).  Hence 
x  =  73°  28' .9. 

RULE.  To  find  an  angle  when  one  of  its  trigonometric  functions  is  given:  select 
from  the  table  the  same  named  function  which  is  next  less  than  the  given  function, 
noting  the  corresponding  angle  and  the  tabular  difference;  compute  the  actual 
difference  (between~the  selected  value  of  the  function  and  the  given  value)  and  divide 


§12]  TRIGONOMETRIC  FUNCTIONS  xiii 

it  by  the  tabular  difference;  this  gives  the  correction  which  is  to  be  added  if  the  given 
function  is  sine  or  tangent,  and  to  be  subtracted  if  the  given  function  is  cosine  or 
cotangent. 

III.     FIVE-PLACE  COMMON  LOGARITHMS  OF  THE 
TRIGONOMETRIC  FUNCTIONS 

12.  Use  of  the  Table.  If  it  is  required  to  find  the  numerical  value  of 
x  =  27.85  X  sin  51°  27',  we  may  apply  logarithms  as  follows: 

log  27.85  =  1.44483. 
log  sin  51°  27'  =  9.89324  -  10  (add) 

log  x  =  1.33807  x  =  21.78 

The  only  new  idea  here  is  the  method  of  finding  log  sin  51°  27',  which  means 
the  logarithm  of  the  sine  of  51°  27'.  The  most  obvious  way  is  to  find  in  Table  II, 
sin  51°  27'  =  0.78206,  and  then  to  find  in  Table  I,  log  0.78206  =  9.89324  -  10, 
but  this  involves  consulting  two  tables.  To  avoid  the  necessity  of  doing  this, 
Table  III  gives  the  logarithms  of  the  sines,  cosines,  tangents,  and  cotangents. 
The  arrangement  and  the  principles  of  interpolation  are  similar  to  those  given 
on  p.  vii  for  Table  I.  The  sines  and  cosines  of  all  acute  angles,  the  tangents 
of  all  acute  angles  less  than  45°  and  the  cotangents  of  all  acute  angles  greater 
than  45°  are  proper  fractions,  and  their  logarithms  end  with  —10,  which  is 
not  printed  in  the  table,  but  which  should  be  written  down  whenever  such  a 
logarithm  is  used. 

In  the  printed  table,  values  are  stated  so  that  10  should  be  subtracted  in  every  case. 

Example  I.     Find  log  sin  68°  25'.4. 

On  the  page  having  68°  at  the  bottom,  and  in  the  row  having  25'  on  the  right  find  log  sin 
68°  25'  =  9.96843  —  10;  the  tabular  difference  is  5;  0.4  X  5  is  given  in  the  margin  as  2;  this  is 
the  correction  to  be  added,  giving  log  sin  68°  25'.4  =  9.96845  —  10. 

(In  case  of  sine  and  tangent  add  the  correction.  In  case  of  cosine  and  cotangent,  subtract 
the  correction.) 

Example  2.     Given  log  cos  x  =  9.72581  —  10,  to  find  x. 

The  logarithmic  cosine  next  less  than  the  given  one  is  9.72562  —  10  and  belongs  to  57°  53'; 
the  actual  difference  is  19;  the  tabular  difference  is  20;  hence  the  correction  is  19/20  =  1.0 
(to  the  nearest  tenth) ;  (subtract) ;  hence  x  =  57°  52'.0. 

In  finding  log  ctn  a  for  any  angle  a,  note  that  log  ctn  a  =  —log  tan  a,  since 
ctn  a  =  I/tan  a.  Hence  the  tabular  differences  for  log  ctn  are  precisely  the  same 
as  those  for  log  tan  throughout  the  table,  but  taken  in  reversed  order.  Likewise, 
log  sec  a.  =  —log  cos  a,  log  esc  a  =  —log  sin  a;  hence  the  values  of  log  sec  a. 
and  log  esc  a  are  omitted. 

For  angles  near  0°  or  near  90°,  the  interpolations  are  not  very  accurate  if 
the  differences  are  large.  For  the  calculation  of  sine  or  tangent  near  0°, 
Table  Ilia,  page  45,  gives  the  values  of 

S  =  log  sin  A  —  log  A'        and        T  =  log  tan  A  —  log  A', 
where  A  is  the  given  angle  and  A'  is  the  number  of  minutes  in  A,  for  values  of 
A  between  0°  and  3°.     Then 

log  sin  A  =  log  A'  +  S        and        log  tan  A  =  log  A'  +  T, 
for    small    angles.     Moreover,   since  we    have    cos  A  =  sin  (90°  —  A)   and 
ctn  A  =  tan  (90°  -  A). 


xiv  EXPLANATION  OF  THE  TABLES  [§12 

log  cos  A  =  log  (90°  -AY  +8        and        log  ctn  A  =  log  (90°  -  A)'  +  T, 

when  A  is  near  90°. 

Another  method  practically  equivalent  to  the  preceding  is  to  use  the  ap- 
proximate relations 

log  sin  A  —  log  sin  B  =  log  A'  —  log  B' 
and 

log  tan  A  —  log  tan  B  =  log  A'  —  log  B', 

vrhere  A  is  the  given  angle  and  B  is  the  nearest  angle  to  A  that  is  given  in  the 
table.  If  A  <  3°  and  |  A  —  B  \  <  1',  these  formulas  give  log  sin  A  and 
log  tan  A  to  five  decimal  places. 

IV-V.    RADIAN  MEASURE 

13.  Computations  in  Radian  Measure.  The  reduction  of  degrees  to  radians 
is  facilitated  by  Table  IV — Conversion  of  Degrees  to  Radians.  Since  TT  radians 
=  180°,  this  table  may  be  regarded  as  a  table  of  multiples  of  ir/180. 

The  values  of  sin  x,  cos  x,  tan  x,  are  stated  for  every  angle  x  from  0.00 
to  1.60  radians  at  intervals  of  0.01  radian  in  Table  V — Trigonometric 
Functions  in  Radian  Measure.  The  values  of  any  of  these  functions  for  larger 
values  of  x  may  be  computed  by  first  converting  the  value  of  the  angle  in 
radian  measure  to  degree  measure,  by  Table  Va,  and  then  finding  the  value 
of  the  function  from  Table  II. 

The  reduction  of  radians  to  degrees  can  be  performed  directly  by  Table  V; 
or,  for  greater  accuracy,  by  the  supplementary  Table  Va. 

VI.    POWERS— ROOTS— RECIPROCALS     ty_: 


\   • 
uare,  c 


14.  Arrangement.    This  table  is  arranged  so  that  the  square,  cube,  square  , 
root,  cube  root,  or  reciprocal  can  be  read  directly  to  five  decimal  places  for 
any  number  n  of  three  significant  figures.     To  attain  this,  not  only  n2,  n3,  Vw, 
•\fn,  1/n,  but  also  VlOn,  -v'lOn,  -v'lOOn  are  printed  on  every  page.    All  values 
have  been  carefully  recomputed  and  checked. 

Thus  to  find  Vl.17,  read  in  Vn  column  the  result:  1.08167.  To  find  Vll.7,  read  in  the  same 
line,  in  VlOn  column  the  result:  3.42053.  To  find  VTl7,  read  10  times  the  entry  in  Vn  column, 
since  VTl7  =  10  VTl7. 

Similarly,  -\J1.17  =  1.05373  from  -^/n  column;  -y^ll.7  =  2.27019  from  the  same  line  in  -\llOn 
column;  -^117  =  4.89097  from  the  same  line  in  VlOOn  column. 

The  effect  of  a  change  in  the  decimal  point  in  n2,  n3,  and  1/n  is  only  to  shift 
the  decimal  point  in  the  result,  without  altering  the  digits  printed. 

VII.    NAPIERIAN  OR  NATURAL  LOGARITHMS 

15.  The  Base  e.  —  Natural  Logarithms.     The  number  e  =  2.7182818  •  •  • 
is  called  the  natural  base  of  logarithms.     The  logarithms  of  numbers  to  this 
base  are  given  in  Table  VII  at  intervals  of  0.01  from  0.01  to  10.09,  and  at  unit 
intervals  from  10  to  409.     The  fundamental  relation  log«  n  =  loge  10  X  logic  n 
enables  us  to  transfer  from  the  base  10  to  the  base  e,  or  conversely;  where 
log.  10  =  2.30258509  ••-. 


§19]  OTHER  TABLES  XV 

VIII.     MULTIPLES  OF  M  AND  OF  1/M 

16.  Multiples  of  M  and  1/M.  This  table  is  convenient  whenever  a  number 
is  to  be  multiplied  by  M  or  by  1/Af.  This  occurs  whenever  it  is  desired  to 
change  from  common  logarithms  to  natural  logarithms,  or  conversely,  since 
M  =  logio  e  and  since  we  have 

log™  x  =  (loge  2)  (logio  «)  =  M  loge  x        and        loge  x  =  (II  M)  log™  x. 

Other  formulas  that  require  these  multiples  are 

logio  e*  -  x  logic  e  =  x-  M        and        loge  (10n'x)  =  log,  x  -f-  n(l/Af); 
and  the  approximate  formulas  (see  §§  8,  9,  pp.  x,  xi) 

logio  (1  ±  x)  =  ±x-Af        and        10**  =  1  ±  (l/Af)z. 


IX.    VALUES  AND  LOGARITHMS  OF  HYPERBOLIC  FUNCTIONS 

17.  Hyperbolic  Functions.     This  table  gives  the  values  of  e*,  e~~*,  sinh  x, 
cosh  x,  tanh  x;  and  the  logarithms  of  ex,  sinh  x,  cosh  z,  at  varying  intervals 
from  x  =  0  to  x  =  10.     It  is  to  be  noted  that  log  e~x  =  —  log  e*  and  log  tanh  x 
=  log  sinh  x  —  log  cosh  x.     The  table  may  be  extended  indefinitely  by 
means  of  Table  VIII,  since  Iog10  e*  =  x-  M;  for  this  reason  Table  VIII  may  be 
regarded  as  a  table  of  values  of  logio  e*. 

X.    VALUES  AND  LOGARITHMS  OF  HAVERSINES 

18.  Haversines.     This  table  gives  the  values  and  the  logarithms  of  the 
haversines  of  angles  from  0°  to  180°  at  intervals  of  10'.     The  haversine,  which 
means  half  of  the  versed  sine,  is 

hav  A  =  (Yd  vers  A  =  (Y^)(l  -  cos  A); 

hence  its  values  to  five  places  may  be  computed  from  the  table  of  cosines. 
It  is  used  extensively  in  navigation,  and  it  may  be  used  to  advantage  in  the 
solution  of  ordinary  oblique  triangles. 

XI.    FACTOR  TABLE—  LOGARITHMS  OF  PRIMES 

19.  Factors  of  Composite  Numbers.     Logarithms  of  Primes.     The  uses 
of  this  table  are  evident  in  questions  involving  factoring,  and  for  finding  high- 
place  logarithms  of  numbers  whose  prime  factors  are  less  than  2018. 

We  shall  illustrate  the  finding  of  logarithms  of  other  numbers  by  finding 
log  IT.  Taking  w  =  3.14159  26536,  divide  by  3  (the  first  digit),  obtaining 
1.04719  75512  •  •  •.  Divide  this  quotient  by  1.047  (in  general,  by  the  nearest 
first  four  digits),  obtaining  1.00018  8683  •••.  By  Table  VIII,  the  approxi- 
mate formula  log  (1  ±  x)  =  ±X'M  gives 

log  1.00018  8683    =  0.00008  1944  (Table  VIII) 

log  3  =  0.47712  12547  (Table  XI) 

log  1.047  =  log  3  +  log  0.349  =  0.01994  66817  (Table  XI) 

log  TT  =  0.49714  9880 

while  the  true  value  of  log  IT  is  0.49714  98726  9,  so  that  the  error  is  less  than  1  in 
the  eighth  place.  In  general,  this  process  will  give  the  logarithm  of  any  number 
to  within  6  in  the  eighth  decimal  place,  and  the  probable  error  is  less  than  1.5 
in  the  eighth  place.  For  still  greater  accuracy,  see  Table  la  and  §  10. 


xvi  EXPLANATION  OF  THE  TABLES  [§20 

XII.     INTEREST  TABLES 

20.  Interest  Tables.     Tables  XII  a,  b,  c,  d  give  compound  interest  and 
annuity  data  for  various  per  cents  up  to  fifty  years.     Aside  from  the  obvious 
uses,  formulas  involving  these  data  will  be  found  in  works  on  statistics,  ac- 
counting, and  the  mathematics  of  business. 

Table  XHe  gives  the  logarithms  of  (1  +  r)  to  fifteen  places,  for  all  ordinary 
values  of  r  from  J^%  to  10%.  For  other  values  of  r,  log  (1  +  r)  may  be 
computed  from  Table  la  (see  §  8).  The  final  result  in  interest  calculations 
may  be  obtained  to  nine  significant  figures  by  the  antilogarithms  of  Table  la 
(see  §  9). 

Table  XII/  is  the  American  Experience  Mortality  Table. 

XIV.    FOUR-PLACE  TABLES 

21.  Four-place  Tables.     These  are  duplicates  of  the  preceding  five-place 
tables,  reduced  to  four  places,  and  with  larger  intervals  between  the  tabulations. 
The  value  of  such  four-place  tables  consists  in  the  greater  speed  with  which 
they  can  be  used,  in  case  the  degree  of  accuracy  they  afford  is  sufficient  for 
the  purpose  in  hand. 

XIVo.  Logarithms  of  Numbers.  The  only  special  feature  of  this  table 
is  that  the  proportional  parts  are  printed  for  every  tenth  in  every  row;  hence  the 
logarithm  of  any  number  of  four  significant  figures  can  be  read  directly. 

XIV6.  Antilogarithms.  This  table  will  be  found  to  facilitate  approximate 
calculations  to  a  marked  degree.  The  proportional  parts  are  stated  in  the 
right-hand  margin  for  each  row  separately.  This  arrangement,  with  the 
corresponding  one  in  Table  XlVa,  makes  the  tables  effectively  four-place  each 
way. 

XIVc.  Values  and  Logarithms  of  Trigonometric  Functions.  In  this  table, 
the  values  of  sin  a,  cos  a,  tan  a,  ctn  a,  and  their  common  logarithms,  are  stated 
for  each  10-minute  interval  in  a.  The  characteristics  of  the  logarithms  are 
omitted,  since  they  can  be  supplied  readily  from  the  value. 


Greek  Alphabet 

LETTERS  NAMES  LETTERS  NAMES  LETTERS    NAMES  LETTERS    NAMES 


A 

a 

Alpha 

H 

•n 

Eta 

N 

V 

Nu 

T 

r 

Tau 

B 

0 

Beta 

e 

e 

Theta 

g 

% 

Xi 

T 

V 

Upsilon 

r 

7 

Gamma 

i 

t 

Iota 

0 

0 

Omicron 

* 

0 

Phi 

A 

5 

Delta 

K 

K 

Kappa 

n 

IT 

Pi 

X 

X 

Chi 

E 

e 

Epsilon 

A 

X 

Lambda 

p 

P 

Rho 

* 

* 

Psi 

Z     f     Zeta  M    M    Mu  S     o-  s   Sigma  fl     w     Omega 


LOGARITHMIC  AND 
TRIGONOMETRIC   TABLES 


TABLE  I 
COMMON  LOGARITHMS  OF  NUMBERS 

FROM 

1    TO    10  000 
TO 

FIVE  DECIMAL  PLACES 
1  —  100 


N 

Log 

N 

Log 

N 

Log 

N 

Log 

N 

Log 

0 

20 

1.30  103 

40 

1.60206 

60 

1.77815 

80 

1.90  309 

1 
2 
3 

0.00  000 
0.30  103 
0.47  712 

21 
22 
23 

1.32  222 
1.34  242 
1.36  173 

41 
42 
43 

1.61  278 
1.62  325 
1.63  347 

61 
62 
63 

1.78  533 
1.79  239 
1.79  934 

81 
82 
83 

1.90849 
1.91  381 
1.91  908 

4 
5 
6 

0.60  206 
0.69  897 
0.77  815 

24 
25 
26 

1.38  021 
1.39  794 
1.41  497 

44 
45 
46 

1.64  345 
1.65  321 
1.66276 

64 
65 
66 

1.80  618 
1.81  291 
1.81  954 

84 
85 
86 

1.92  428 
1.92  942 
1.93  450 

7 
8 
9 

0.84510 
0.90  309 
0.95  424 

27 

28 
29 

1.43  136 
1.44716 
1.46  240 

47 
48 
49 

1.67  210 
1.68  124 
1.69  020 

67 
68 
69 

1.82  607 
1.83  251 
1.83  885 

87 
88 
89 

1.93  952 
1.94  448 
1.94  939 

10 

1.00  000 

30 

1.47  712 

50 

1.69  897 

70 

1.84510 

90 

1.95424 

11 
12 
13 

1.04  139 
1.07918 
1.11  394 

31 
32 
33 

1.49  136 
1.50515 
1.51  851 

51 
52 
53 

1.70  757 
1.71  600 
1.72  428 

71 
72 
73 

1.85  126 
1.85  733 
1.86  332 

91 
92 
93 

1.95  904 
1.96  379 
1.96  848 

14 
15 
16 

1.14  613 
1.17  609 
1.20412 

34 
35 

36 

1.53  148 
1.54  407 
1.55  630 

54 

55 
56 

1.73  239 
1.74  036 
1.74  819 

74 
75 
76 

1.86  923 
1.87  506 
1.88  081 

94 

95 
96 

1.97  313 
1.97  772 
1.98227 

17 
18 
19 

1.23  045 
1.25  527 
1.27  875 

37 
38 
39 

1.56  820 
1.57  978 
1.59  106 

57 

58 
59 

1.75  587 
1.76  343 
1.77  085 

77 
78 
79 

1.88  649 
1.89  209 
1.89  763 

97 
98 
99 

1.98  677 
1.99  123 
1.99  564 

N 

Log 

N 

Log 

N 

Log 

N 

Log 

N 

Log 

2  100  —  Logarithms  of  Numbers  —  150 

\   c;    1    =     "^ 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop.  Pts. 

100 

00000 

043 

087 

130 

173 

217 

260 

303 

346 

389 

101 

432 

475 

518 

561 

604 

647 

689 

732 

775 

817 

44 

43 

48 

102 

860 

903 

945 

988 

*030 

*072 

*115 

*157 

*199 

*242 

1 

4.4 

4.3 

4.2 

103 

01284 

326 

368 

410 

452 

494 

536 

578 

620 

662 

2 

8.8 

8.6 

8.4 

104 
105 

703 
02119 

745 
160 

787 
202 

828 
243 

870 

284 

912 
325 

953 
366 

025=. 

30r 

^036 
"449" 

*078 
490 

3 
4 

13.2 
17.6 

12.9 
17.2 

12.6 
16.8 

106 

531 

572 

612 

653 

694 

735 

776 

816 

857 

898 

5 
6 

22.0 
26.4 

21.5 
25.8 

21.0 
25.2 

107 

938 

979 

*019 

*060 

*100 

*141 

*181 

*222 

*262 

*302 

7 

30.8 

30.1 

29.4 

108 

03342 

383 

423 

463 

503 

543 

583 

623 

663 

703 

8 

35.2 

34.4 

33.6 

109 

743 

782 

822 

862 

902 

941 

981 

*021 

*060 

*100 

9 

39.6 

38.7 

37.8 

110 

04139 

179 

218 

258 

297 

336 

376 

415 

454 

493 

111 

532 

571 

610 

650 

689 

727 

766 

805 

844 

883 

** 

«U 

09 

112 

922 

961 

999 

*038 

*077 

*115 

*154 

*192 

*231 

*269 

1 

4:1 

4.0 

3.9 

113 

05308 

346 

385 

423 

461 

500 

638 

576 

614 

652 

2 

8,£ 

8.0 

7.8 

114 

690 

729 

767 

805 

843 

881 

918 

956 

994 

*032 

3 

12.3 

12.0 

11.7 

115 

06070 

108 

145 

183 

221 

258 

296 

333 

371 

408 

4 

16.4 

16.0 

15.6 

116 

446 

483 

521 

558 

^595 

633 

670 

707 

744 

781 

5 
6 

20..5 
24.6 

20.0 
24.0 

19.5 
23.4 

117 

819 

856 

893 

930 

*967 

*004 

*041 

*078 

*115 

*151 

7 

28.7 

28.0 

27.3 

118 

07188 

225 

262 

298 

335 

372 

408 

445 

482 

518 

8 

32.8 

32.0 

31.2 

119 

555 

591 

628 

664 

700 

737 

773 

809 

846 

882 

9 

36.9 

36.0 

35.1 

120 

918 

954 

990 

*027 

*063 

*099 

*135 

*171 

*207 

*243 

121 

08279 

314 

350 

386 

422 

458 

493 

529 

565 

600 

SB 

3Y 

at) 

122 

636 

672 

707 

743 

778 

814 

849 

884 

920 

955 

1 

3.8 

3.7 

g~g 

123 

991 

*026 

*061 

*096 

*132 

*167 

*202 

*237 

*272 

*307 

2 

7.6 

7.4 

7*.2 

124 

09342 

377 

412 

447 

482 

517 

652 

687 

621 

656 

3 

11.4 

11.1 

10.8 

125 

691 

726 

760 

795 

830 

864 

899 

934 

968 

*003 

4 

15.2 

14.8 

14.4 

126 

10037 

072 

106 

140 

175 

209 

243 

278 

312 

346 

5 

6 

19.0 

22.8 

18.5 
22.2 

18.0 
21.6 

127 

380 

415 

449 

483 

517 

551 

585 

619 

653 

687 

7 

26.6 

25.9 

25.2 

128 
129 

721 
11059 

755 
093 

789 
126 

823 
160 

857 
193 

890 
~22T 

h924 
261 

958 
294 

992 
327 

*025 
361 

8 
9 

30.4 
34.2 

29.6 
33.3 

28.8 
32.4 

130 

394 

428 

461 

494 

528 

561 

594 

628 

661 

694 

131 

727 

760 

793 

826 

860 

893 

926 

959 

992 

*024 

35 

34 

33 

132 

12057 

090 

123 

156 

189 

222 

254 

287 

320 

352 

1 

3.5 

3.4 

3.3 

133 

385 

418 

450 

483 

516 

548 

681 

613 

646 

678 

2 

7.0 

6.8 

6.6 

134 

710 

743 

775 

808 

840 

872 

905 

937 

969 

*001 

3 

10.5 

10.2 

9.9 

135 

13033 

066 

098 

130 

162 

194 

226 

258 

290 

322 

4 

14.0 

13.6 

13.2 

136 

354 

386 

418 

450 

481 

513 

645 

677 

609 

640 

5 

17.5 

17.0 

16.5 

6 

21.0 

20.4 

19.8 

137 

672 

704 

735 

767 

799 

830 

862 

893 

925 

956 

7 

24.5 

23.8 

23.1 

138 

988 

*019 

*051 

*082 

*114 

*145 

*176 

*208 

*239 

*270 

8 

28.0 

27.2 

26.4 

139 

14301 

333 

364 

395 

426 

457 

489 

520 

551 

582 

9 

31.5 

30.6 

29.7 

140 

613 

644 

675 

706 

737 

768 

799 

829 

860 

891 

1 

V 

/3.2 

31 
3.1 

30 

3.0 

141 
142 

922 
15229 

953 

259 

983 
290 

*014 
320 

*045 
351 

*076 
381 

412 

*137 
442 

*168 
473 

*198 
503 

143 

634 

564 

594 

625 

655 

685 

7HT 

746 

776 

806 

2 

6.4 

6.2 

6.0 

144 

836 

866 

897 

927 

957 

987 

*017 

^047 

*077 

*107 

3 

9.6 

9.3 

9.0 

145 

16137 

167 

197 

227 

256 

286 

316 

346 

376 

406 

4 

12.8 

12.4 

12.0 

146 

435 

465 

495 

524 

554 

584 

613 

643 

673 

702 

5 

16.0 

15.5 

15.0 

6 

19.2 

18.6 

18.0 

147 

732 

761 

791 

820 

850 

879 

909 

938 

967 

997 

7- 

22.4 

21.7 

21.0 

148 

17026 

056 

085 

114 

143 

173 

202 

231 

260 

289 

8 

25.6 

24.8 

24.0 

149 

319 

348 

377 

406 

435 

464 

493 

522 

551 

580 

9 

28.8 

27.9 

27.0 

150 

609 

638 

667 

696 

725 

754 

782 

811 

840 

869 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop.  Pts. 

150  —  Logarithms  of  Numbers  —  200 


3.01 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop.  Pts. 

150 

17609 

638 

667 

696 

725 

754 

782 

811 

840 

869 

1 
2 
3 
4 
5 
6 
7 
S 
9 

1 

2 
3 
4 
5 
6 
7 
8 
9 

1 

2 
3 
4 
5 
6 
7 
8 
9 

1 
2 
3 
4 
5 
6 
7 
S 
9 

1 
2 
3 

4 
5 
6 

7 
8 
9 

29 

2.9 

5.8 
8.7 
11.6 
14.5 
17.4 
20.3 
23.2 
26.1 

27 

2.7 
5.4 
8.1 
10.8 
13.5 
16.2 
18.9 
21.6 
24.3 

25 

2.5 

5.0 
7.5 
10.0 
12.5 
15.0 
"17.5 
20.0 
22.5 

23 

2.3 

4.6 
6.9 
9.2 
11.5 
13.8 
16.1 
18.4 
20.7 

21 

2.1 

4.2 
6.3 
8.4 
10.5 
12.6 
14.7 
16.8 
18.9 

28 

2.8 
5.6 
8.4 
11.2 
14.0 
16.8 
19.6 
22.4 
25.2 

26 

2.6  : 
5.2 

10.4. 
13.0  ' 
15.6 
18.2 
20.8 
23.4 

24 

2.4 
4.8 
7.2 
9.6 
12.0 
14.4 
16.8 
19.2 
21.6 

22 

2.2  , 
4.4 
6.6 
8.8 
11.0 
13.2 
15.4 
17.6 
19.8 

151 
152 
153 

154 
155 
156 

157 
158 
159 

898 
18184 
469 

752 
19033 
312 

590 
866 
20140 

926 
213 

498 

780 
061 
340 

618 
893 
167 

955 
241 
526 

808 
089 
368 

645 
921 
194 

984 
270 
554 

837 
117 
396 

673 

948' 
222 

*013 
298 
583 

865 
145 
424 

700 
976 

249 

*041 
327 
611 

893 
173 
451 

728 
*003 
276 

*070 
355 
639 

921 
201 
479 

756 
*030 
303 

*099 
384 
667 

949 
229 
507 

783 
*058 
330 

*127 
412 
696 

977 
257 
535 

811 
*085 
358 

*156 
441 
724 

*005 
285 
562 

838 
*112 
385 

160 

412 

439 

466 

493 

520 

548 

575 

602 

629 

656 

161 
162 
163 

164 
165 
166 

167 

168 
169 

683 
952 
21219 

484 
748 
22011 

272 
531 

789 

710 
978 
245 

511 
775 
037 

298 
557 

814 

737 
*005 
272 

537 
J&OJ. 
063 

324 

583 
840 

763 
*032 
299 

564 
827 
089 

350 
608 
866 

790 
*059 
325 

590 
854 
115 

376 
634 
891 

817 
*085 
352 

617 
880 
141 

401 
660 
917 

844 
*112 
378 

643 
906 
167 

427 
686 
943 

871 
*139 
405 

669 
932 
194 

453 
712 
968 

898 
*165 
431 

696 

958 
220 

479 
737 
994 

925 
*192 
458 

722 
985 
246 

505 
763 
*019 

170 

23045 

070 

096 

121 

147 

172 

198 

223 

249 

274 

171 
172 
173 

174 
175 
176 

177 
178 
179 

300 
553 
805 

24055 
304 
551 

797 
25042 
285 

325 
578 
830 

080 
329 
576 

822 
066 

310 

350 
603 
855 

105 
353 
601 

846 
091 
334 

376 
629 
880 

130 
378 
625 

871 
115 
358 

401 
654 
905 

155 

403 
650 

895 
139 
382 

426 
679 
930 

180 
428 
674 

920 
164 

406 

452 
704 
955 

204 
452 
699 

944 
188 
431 

477 
729 
980 

229 
477 
724 

969 
212 
455 

502 
754 
*005 

254 
502 

748 

993 

237 
479 

528 
779 
*030 

279 
627 
773 

*018 
261 
503 

180 

527 

551 

575 

600 

624 

648 

672 

696 

720 

744 

181 
182 
183 

184 
185 
186 

187 
188 
189 

768 
26007 
245 

482 
717 
951 

27184 
416 
646 

792 
031 
269 

505 
741 
975 

207 
439 
669 

816 
055 
293 

529 
764 
998 

231 
462 
692 

840 
079 
316 

553 

788 
*021 

254 

485 
715 

864 
102 
340 

576 
811 
*045 

277 
508 
738 

888 
126 
364 

600 
834 
*068 

300 
531 
761 

912 
150 
387 

623 

858 
*091 

323 
554 

784 

935 
174 
411 

647 
881 
*114 

346 

577 

807 

959 
198 
435 

670 
905 
*138 

370 
600 
830 

983 
221 
458 

694 
928 
*161 

393 
623 
852 

190 

875 

898 

921 

944 

967 

989 

*012 

*035 

*058 

*081 

191 
192 
193 

194 
195 
196 

197 
198 
199 

28103 
330 
556 

780 
29003 
226 

447 
667 

885 

126 
353 
578 

803 
026 
248 

469 
688 
907 

149 
375 
601 

825 
048 
270 

491 
710 
929 

171 
398 
623 

847 
070 
292 

513* 
732 
951 

194 
421 
646 

870 
092" 
314 

535 

754 
973 

217 
443 
668 

892 
115 
336 

557 
776 
994 

240 
466 
691 

914 
137 
358 

579 

70S 
*016 

262 
488 
713^ 

93V 
159 
380 

601 
820 
*038 

285 
511 
735 

959 
181 
403 

623 

842 
*060 

307 
533 

758 

981 
203 
425 

645 
863 

*081 

200 

30  103 

125 

146 

168 

190 

211 

233 

255 

276 

298 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop.  Pts. 

200  —  Logarithms  of  Numbers  —  250 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop.  Pts. 

200 

30  103 

125 

146 

168 

190 

211 

233 

255 

276 

298 

1 

1 
2 
3 
4 
5 
6 
7 
8 
9 

1 

2 
3 
4 
5 
6 
7 
8 

7 

i 

2 
3 
.4. 
5 

6 

7 
8 
9 

os  2 
50102 

22; 

2.2 
4.4 
6.6 
8.8 
11.0 
13.2 
15.4 
17.6 
19.8 

20 

2.0 
4.0 
6.0 
8.0 
10.0 
12.0 
14.0 
16.0 
18.0 

18 

1.8 
3.6 
5.4 
7.2 
9.0 
10.8 
12.6 
14.4 
16.2 

99957 

21 

2.1 
4.2 
6.3 
8.4 
10.5 
12.6 
14.7 
16.8 
18.9 

yp 

1.9 
3.8 
5.7 
7.6 
9.5 
11.4 
13.3 
15.2 
17.1 

17 

1.7 
3.4 
5,1 
6.8 
8.5 
10.2 
11.9 
13.6 
15.3 

201 
202 
203 

204 
205 
206 

207 
208 
209 

320 
535 
750 

963 
31  175 
387 

597 
806 
32015 

341 
557 
771 

984 
197 
408 

618 
827 
035 

363 
578 
792 

*006 
218 
429 

639 

848 
056 

384 
600 

814 

*027 
239 
450 

660 
869 

077 

406 
621 
835 

*048 
260 
471 

681 
890 
098 

428 
643 
856 

*069 
281 
492 

702 
911 
118 

449 
664 

878 

*091 
302 
513 

723 
931 
139 

471 
685 
899 

*112 
323 
534 

744 
952 
160 

492 
707 
920 

*133 
345 
555 

^765 

Sf 

514 
728 
942 

*154 
366 
576 

*785. 
994 
201 

210 

222 

243 

263 

284 

305 

325 

346 

366 

387 

408 

211 
212 
213 

214 
215 
216 

217 
218 
219 

428 
634 
838 

33041 
244 
445 

646 
846 
34044 

449 
654 

858 

062 
264 
465 

666 
866 
064 

469 
675 

879 

082 
284 
486 

686 

885 
084 

490 
695 
899 

102s 
304 

506 

706 
905 
104 

510 
715 
919 

122 
325 
526 

726 
925 
124 

531 
736 
940 

143 
345 
546 

746 
945 
143 

552 
756 
960 

163 
365 
566 

766 
965 
163 

572 
777 
980 

183 

385 
586 

786 
985 
183 

593 
797 
*001 

203 
405 
606 

806 
*005 
203 

613 
818 
*021 

224 
425 
626 

826 

*025 
223 

220 

242 

262 

282 

301 

321 

341 

361 

380 

400 

420 

221 
222 
223 

224 
225 
226 

227 
228 
229 

439 
635 
830 

35025 
218 
411 

603 
793 

984 

459 
655 
850 

044 
238 
430 

622 
813 
*003 

479 
674 
869 

064 
257 
449 

641 
832 
*021 

498 
694 
889 

083 
276 

468 

660 
851 
*040 

518 
713 
908 

102 
295 

488 

679 
870 
*059 

537 
733 
928 

122 
315 
507 

698 

889 
*078 

557 
753 
947 

141 
334 
526 

717 

908 
*097 

577 
772 
967 

160 
353 
545- 

736 
927 
*116 

596 
792 
986 

180 
372 

564 

755 
946 
*135 

616 
811 
*005 

199 
392 
583 

774 
965 
*154 

230 

36173 

192 

211 

229 

248 

267 

286 

305 

324 

342 

231 
232 
233 

234 
235 
236 

237 
238 
239 

361 
549 
736 

922 
37107 
291 

475 

658 
840 

380 
568 
754 

940 
125 
310 

493 
676 

858 

399 
•586 
773 

959 
144 
328 

511 
694 

876 

418 
605 
791 

977 
162 
346 

530 

712 
894 

436 
624 
810 

996 
181 
365 

548 
731 
912 

455 
642 
829 

*014 
199 
383 

566 
749 
931 

474 
661 
847 

*033 
218 
401 

585 
767 
949 

493 
680 
866 

*051 
236 
420 

603 

785 
967 

511 
698 

884 

*070 
254 
438 

621 

803 
985 

530 
717 
903 

*088 
273 
457 

639 

822 
*003 

240 

38021 

039 

057 

075 

093 

112 

130 

148 

166 

184 

241 
242 
243 

244 

245 
246 

247 
248 
249 

202 
382 
561 

739 
917 
39094 

270 

445 
620 

220 
399 
578 

757 
934 
111 

287 
463 
637 

238 
417 
596 

775 
952 
129 

305 
480 
655 

256 
435 
614 

792 
970 
146 

322 

498 
672 

274 
453 
632 

810 
987 
164 

340 
515 
690 

292 
471 
650 

828 
*005 
182 

358 
533 

707 

31Q_ 

489 
668 

846 
*023 
199 

375 
550 

724 

328 
507 
686 

863 
*041 
217 

393 

568 

742 

346 

525 
703 

881 
*058 
235 

410 

585 
759 

364 
543 
721 

899 
*076 
252 

428 
602 

777 

250 

794 

811 

829 

846 

863 

881 

898 

915 

933 

950 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop.  Pts. 

n 


50  —  Logarithms  of  Numbers 


—  300^- 


(90 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop.  Pts. 

250 

39794 

811 

829 

846 

863 

881 

898 

915 

933 

950 

1 

2 
3 
4 
5 
6 
7 
8 
9 

J 

=1 
=1 

1 
2 
3 
4 
5 
5 
7 
8 
9 

1 
2 
3 
4 
5 
6 
7 
8 
9 

18 

1.8 
3.6 
5.4 
7.2 
9.0 
10.8 
12.6 
14.4 
16.2 

\t 

3gwe 

3glO  2. 

13429 

16. 

i.6 

3.2 

4.8 
6.4 
8.0 
9.6 
11.2 
12.8 
14.4 

14 

1.4 

2.8 
4.2 
5.6 
7.0 
8.4 
9.8 
11.2 
12.6 

f* 

3.4 
5.1 
6.8 
8.5 
10.2 
11.9 
13.6 
15.3 

ris-  •  • 

44819 

15 

1.5 
3.0 
4.5 
6.0 
7.5 
9.0 
10.5 
12.0 
13.5 

251 
252 
253 

254 
255 
256 

257 
258 
259 

967 
40140 
312 

483 
654 
824 

993 
41  162 
330 

985 
157 
329 

500 
671 
841 

*010 
179 
347 

*002 
175 
346 

518 
688 
858 

*027 
196 
363 

*019 
192 
364 

535 
705 

875 

*037 
209 
381 

552 
722 
892 

*054 
226 
398 

569 
739 
909 

*078 
246 
414 

*071 
243 
415 

586 
756 
926 

*095 
263 
430 

*088 
261 
432 

603 
773 
943 

*111 

280j 
4*7- 

*106 
278 
449 

620 
790 
960 

*128 
296 
,464 

*123 
295 
466 

637 
807 
976 

*145 
313 
481 

~647~ 

*044 
212 
380 

.*061 

22& 
397 

260 

497 

514 

531 

547 

564 

581 

597 

614 

'631 

261 
262 
263 

264 
265 
266 

267 
268 
269 

664 
830 
996 

42160 
325 

488 

651 
813 
975 

681 
847 
*012 

177 
341 
504 

667 
830 
991 

697 
863 
*029 

193 
357 
521 

684 
846 
*008 

714 
880 
*045 

210 
374 

537 

700 
862 
*024 

731 
896 
*062 

226 
390 
553 

716 

878 
*040 

747 
913 
*078 

243 
406 
570 

732 
894 
*056 

764 
929 
*095 

259 
423 
586 

749 
911 

*072 

780 
946 
*111 

275 
439 
602 

765 
927 

*088 

797 
963 
*127 

292 
455 
619 

781 
943 
*104 

814 
979 
*144 

308 
472 
635 

797 
959 
*120 

270 

43136 

152 

169 

185 

201 

217 

233 

249 

265 

281 

271 
272 
273 

274 
275 
276 

277 
278 
279 

297 
457 
616 

775 
933 
44091 

248 
404 
560 

313 
473 
632 

791 
949 
107 

264 
420 
576 

329 
489 
648 

807 
965 
122 

279 
436 
592 

345 
605 
664 

823 
981 
138 

295 
451 
607 

361 
521 
680 

838 
996 
154 

311 

467 
623 

377 
537 
696 

854 
*012 
170 

326 

483 
638 

393 
553 
712 

870 
*028 
185 

342 

498 
654 

409 
569 

727 

886 
*04)t 
201 

358 
514 
669 

425 
584 
743 

902 
*059 
217 

373 
529 
685 

441 
600 
759 

917 
*075 
232 

389 

545 
700 

280 

716 

731 

747 

762 

778 

793 

809 

824 

840 

855 

281 
282 
283 

284 
285 
286 

287 

288 
289 

871 
45025 
179 

332 
484 
637 

788 
939 
46090 

886 
040 
194 

347 
500 
652 

803 
954 

105 

902 
056 
209 

362 
515 
667 

818 
969 
120 

917 
071 
225 

378 
530 
682 

834 
984 
135 

932 
086 
240 

393 
545 
697 

849 
*000 
150 

948 
102 
255 

408 
561 
712 

864 
*015 
165 

963 
117 
271 

423 
576 

728 

879 
*030 

180 

979 
133 
286 

439 
591 
743 

894 
*045 
195 

994 
148 
301 

454 
606 
758 

909 
*060 
210 

*010 
163 
317 

469 
621 
773 

924 
*075 
225 

290 

240 

255 

270 

285 

300 

315 

330 

345 

359 

374 

291 
292 
293 

294 
295 
296 

297 
298 
299 

389 
538 
687 

835 
982 
47129 

276 
422 
567 

404 
553 
702 

850 
997 
144 

290 
436 

582 

419 
568 
716 

864 
*012 
159 

305 
451 
596 

434 
583 
731 

879 
*026 
173 

319 
465 
611 

449 
598 
746 

894 
*041 

188 

334 

480 

625 

464 
613 
761 

909' 
*056 
202 

349 
494 
640 

479 
627 
'776 

~923 
*070 
217 

363 
509 
654 

494 
642 
790 

938 
*085 
232 

378 
524 

669 

509 
657 
805 

953 
*100 
246 

392 
538 
683 

523 
672 
820 

967 
*114 
261 

407 
553 
698 

300 

712 

727 

741 

756 

770 

784 

799 

813 

828 

842 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop.  Pts. 

300  —  Logarithms  of  Numbers  —  350 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop.  Pts. 

300 

47712 

727 

741 

756 

770 

784 

799 

813 

828 

842 

1 

=•.4 
I 

=.4 

1 

2 
3 
4 
5 
6 
7 
8 
9 

1 
2 
3 
4 
5 
6 
7 
8 
9 

og3 
t7712 

Og  IT 

19714 

15 

1.5 

3.0 
4.5 
6.0 
7.5 
9.0 
10.5 
12.0 
13.5 

13 

1.3 

2.6 
3.9 
6.2 
6.5 
7.8 
9.1 
10.4 
11.7 

12547 

38727 

14 

1.4 
2.8 
4.2 
5.6 
7.0 
8.4 
9.8 
11.2 
12.6 

12- 

1.2 

2.4 
3.6 
4.8 
6.0 
7.2 
8.4 
9.6 
10.8 

301 
302 
303 

304 
305 
306 

307 
308 
309 

857 
48001 
144 

287 
430 
572 

714 
855 

996 

871 
015 
159 

302 
444 
686 

728 
869 
*010 

885 
029 
173 

316 

458 
601 

742 

883 
*024 

900 
044 

187 

330 
473 
615 

756 
897 
*038 

914 
058 
202 

344 

487 
629 

770 
911 
*052 

929 
073 
216 

359 
501 
643 

785 
926 
*066 

943 
087 
230 

373 

515 
657 

799 
940 

*080 

958 
101 
244 

387 
530 
671 

813 
954 
*094 

972 
116 
259 

401 

544 
686 

827 
968 
*108 

986 
130 
273 

416 
558 
700 

841 
982 
*122 

310 

49  136 

150 

164 

178 

192 

206 

220 

234 

248 

262 

311 
312 
313 

314 
315 
316 

317 
318 
319 

276 
415 
554 

693 
831 
969 

50106 
243 
379 

290 
429 
568 

707,. 

304 
443 

582 

721 
859 
996 

133 

270 
406 

318 
457 
696 

734 

872 
*010 

147 
284 
420 

332 
471 
610 

748 
886 
*024 

161 

297 
433 

346 
485 
624 

762 
900 
*037 

174 
311 

447 

360 
499 
638 

776 
914 
*051 

188 
325 
461 

374 
513 
651 

790 

927 
*065 

202 
338 
474 

388 
527 
665 

803 
941 
*079 

215 
352 

488 

402 
541 
679 

817 
955 
*092 

229 
365 
501 

845 
982 

120 
256 
393 

320 

515 

629 

542 

556 

669 

583 

696 

610 

623 

637 

321 
322 
323 

324 
325 
326 

327 
328 
329 

651 

786 
920 

51055 

188 
322 

_  455 

587 
720 

664 
799 
934 

068 
202 
335 

468 
601 
733 

678 
813 
947 

081 
215 
348 

481 
614 
746 

691 
826 
961 

095 

228 
362 

495 

627 
759 

705 
840 
974 

108 
242 
375 

608 
640 

772 

718 
853 
987 

121 

255 
388 

521 

654 
786 

732 
866 
*001 

135 

268 
402 

534 
667 
799 

745 
880 
*014 

148 
283 
415 

648 
680 
812 

759 
893 
*028 

162 
295 

428 

561 
693 
825 

772 
907 
*041 

175 

308 
441 

574 
706 
838 

330 

851 

865 

878 

891 

904 

917 

930 

943 

957 

970 

331 
332 
333 

334 
335 
336 

337 
338 
339 

983 
52114 
244 

375 

504 
634 

763 
892 
53020 

996 
127 

257 

388 
517 
647 

776 
905 
033 

*009 
140 
270 

401 
530 
660 

789 
917 
046 

*022 
153 

284 

414 
543 
673 

802 
930 

058 

*035 
166 
297 

427 
556 
686 

815 
943 
071 

*048 
179 
310 

440 
569 
699 

827 
956 
084 

*061 
192 
323 

453 

682 
711 

840 
969 
097 

*075 
205 
336 

466 
595 
724 

853 
982 
110 

*088 
218 
349 

479 
608 
737 

866 
994 
122 

*101 
231 
362 

492 
621 
750 

879 
*007 
135 

340 

148 

161 

173 

186 

199 

212 

224 

237 

250 

263 

341 
342 
343 

344 
345 
346 

347 
348 
349 

275 
403 
629 

656 

782 
908 

54033 
158 

283 

288 
415 
542 

668 
794 
920 

045 
170 
295 

301 
428 
555 

681" 
807 
933 

058 
183 
307 

314 
441 
667 

694 
820 
945 

070 
195 
320 

326 
453 
580 

706 
832 
958 

083 
208 
332 

339 
466 
593 

719 
845 
970 

095 
220 
345 

352 
479 
605 

732 
857 
983 

108 
233 
357 

364 
491 
618 

744 
870 
996 

120 
245 
370 

377 
504 
631 

757 
882 
*008 

133 

258 
382 

390 
517 
643 

769 
895 
*020 

145 
270 
394 

350 

407 

419 

432 

444 

456 

469 

481 

494 

506 

518 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop.  Pts. 

350  —  Logarithms  of  Numbers  —  400 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop.  Pts. 

350 

54407 

419 

432 

444 

456 

469 

481 

494 

506 

518 

s  ^^ 

13, 

1   1.3 

2   2.6 
3   3.9 
4  5-.2 
3   6.5 
6   7.8 
7   9.1 
8  10.4 
9  11.7 

1 

12 

1.2 
2.4 
3.6 
4.8 
6.0 
7.2 
8.4, 
9.6 
10.8 

10 

1.0 
2.0 
3.0 
4.0 
5.0 
6.0 
7.0 
8.0 
9.0 

351 
352 
353 

354 
355 
356 

357 
358 
359 

531 
654 

777 

900 
55023 
145 

267 

388 
509 

543 

667 
790 

913 
035 
157 

279 
400 
522 

555 
679 

802 

925 
047 
169 

291 
413 
534 

568 
691 
814 

937 
060 
182 

303 
425 
546 

580 
704 

827 

949 
072 
194 

315 

437 
558 

593 

716 
839 

962 
084 
206 

328 
449 
570 

605 
728 
851 

974 
096 
218 

340 
461 
582 

617 

741 
864 

986 
108 
230 

352 
473 
594 

630 
753 
876 

998 
121 
242 

364 
485 
606 

642 
765 

888 

*011 
133 
255 

376 
497 
618 

360 

630 

642 

654 

666 

678 

691 

703 

715 

727 

739 

361 
362 
363 

364 
365 
366 

367 
368 
369 

751 
871 
991 

56110 
229 
348 

467 
585 
703 

763 
883 
*003 

122 
241 
360 

478 
597 
714 

775 
895 
*015 

134 
253 
372 

490 
608 
726 

787 
907 
*027 

146 
265 
384 

502 
620 

738 

799 
919 
*038 

158 
277 
396 

514 
632 
750 

811 
931 
*050 

170 
289 
407 

526 
644 
761 

823 
943 
*062 

182 
301 
419 

538 
656 
773 

835 
955 
*074 

194 
312 
431 

549 

667 
785 

847 
967 
*086 

205 

324 
443 

561 
679 
797 

859 
979 
*098 

217 
336 
455 

573 
691 

808 

370 

820 

832 

844 

855 

867 

879 

891 

902 

914 

926 

//^ 
11- 

1  1.1 
2  2.2 
3  3.3 
4  4.4 
5  5.5 
6  6A 
7  7.7 
8  8.8 
9  9.9 

371 
372 
373 

374 
375 
376 

377 
378 
379 

937 
57054 
171 

287 
403 
519 

634 
749 
864 

949 
066 
183 

299 
415 
530 

646 
761 

875 

961 
078 
194 

310 
426 
542 

657 

772 
887 

972 
089 
206 

322 
438 
553 

669 

784 
898 

984 
101 
217 

334 
449 
565 

680 
795 

910 

996 
113 
229 

345 
461 
576 

692 
807 
921 

*008 
124 
241 

357 

588 

703 
818 
933 

*019 
136 
252 

368 

1484 
600 

715 
830 
944 

*031 
148 
264 

380 
496 
611 

726 
841 
955 

*043 
159 
276 

392 

507 
623 

738 
852 
967 

380 

978 

990 

*001 

*013 

*024 

*035 

*047 

*058 

*070 

*081 

381 
382 
383 

384 
385 
386 

387 
388 
389 

58092 
206 
320 

433 
546 
659 

771 

883 
995 

104 
218 
331 

444 
557 
670 

782 
894 
*006 

115 
229 
343 

456 
569 
681 

794 
906 
*017 

127 
240 
354 

467 
580 
692 

805 
917 

*028 

138 
252 
365 

478 
591 

704 

816 
928 
*040 

149 
263 
377 

490 
602 
715 

827 
939 
*051 

161 
274 
388 

501 
614 
726 

838 
950 

*062 

172 
286 
399 

512 
625 

184 
297 
410 

624 
636 

195 
309 
422 

535 
647 
760 

872 
984 
*095 

-737" 

850 
961 
*073 

749 

861 
973 

*084 

390 

59106 

118 

129 

140 

151 

162 

173 

184 

195 

207 

391 
392 
393 

394 
395 
396 

397 
398 
399 

218 
329 
439 

550 
660 
770 

879 
988 
60097 

229 
340 
450 

561 
671 
780 

890 
999 
108 

240 
351 
461 

572 

682 
791 

901 
*010 
119 

251 
362 
472 

583 
693 
802 

912 
*021 
130 

262 
373 
483 

594 
704 
813 

923 
*032 
141 

273 
384 
494 

605 
715 
824 

934 
*043 
152 

284 
395 
506 

616 
726 
835 

945 

*054 
163 

295 
406 
517 

627 
737 
846 

956 
*065 
173 

306 
417 
528 

638 
748 
857 

966 
*076 
184 

318 
428 
539 

649 
759 
868 

977 
*086 
195 

400 

206 

217 

228 

239 

249 

260 

271 

282 

293 

304 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop.  Pts. 

400  —  Logarithms  of  Numbers  —  450 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop.  Pts. 

400 

60206 

217 

228 

239 

249 

260 

271 

282 

293 

304 

1 
2 
3 
4 
5 
6 
T 
8 
9 

Ic 
=lc 
=9 

1 
2 
3 
4 
5 
6 
7 
8 
9 

11 

1.1 

2.2 
3.3 
4.4 
5.5 
6.6 
7.7 
8.8 
9.9 

g  M 
S  [lo 
6377 
10 

9 

0.9 
1.8 
2.7 
3.6 
4.5 
5.4 
6.3 
7.2 
8.1 

10  * 

1.0 
2.0 
3.0 
4.0 
5.0 
6.0 
7.0 
8.0 
9.0 

ge] 
8431 

401 
402 
403 

404 
405 
406 

407 
408 
409 

314 
423 
531 

638 
746 
853 

959 
61066 
172 

325 
433 
541 

649 

756 
863 

970 
077 
183 

336 
444 
552 

660 
767 
874 

981 

087 
194 

347 
455 
563 

670 

778 
885 

991 
098 
204 

358 
466 
574 

681 

788 
895 

*002 
109 
215 

369 

477 
584 

692 
-Z9& 

379 

487 
595 

703 
810 
917 

*023 
130 
236 

390 
498 
606 

713 

821 
927 

*034 
140 
247 

401 
509 
617 

724 
831 
938 

*045 
151 
257 

412 
520 
627 

735 
842 
949 

*055 
162 
268 

906 

*013 
119 
225 

410 

278 

289 

300 

310 

321 

331 

342 

352 

363 

374 

411 
412 
413 

414 
415 
416 

417 
418 
419 

384 
490 
595 

700 
805 
909 

62014 
118 
221 

395 
500 
606 

711 

815 
920 

024 
128 
232 

405 
511 
616 

721 
826 
930 

034 
138 
242 

416 
521 

627 

731 

836 
941 

045 
149 

252 

426 
532 
637 

742 
847 
951 

055 
159 
263 

437 
542 
648 

752 
857 
962 

066 
170 
273 

448 
553 
658 

763 
868 
972 

076 
180 

284 

458 
563 
669 

773 

878 
982 

086 
190 
294 

469 
574 
679 

784 
888 
993 

097 
201 
304 

479 
584 
690 

794 
899 
*003 

107 
211 
315 

420 

325 

335 

346 

356 

366 

377 

387 

397 

408 

418 

421 
422 
423 

424 
425 
426 

427 
428 
429 

428 
531 
634 

737 
839 
941 

63043 
144 
246 

439 
542 
644 

747 
849 
951 

053 
155 
256 

449 
552 
655 

757 
859 
961 

063 
165 
266 

459 
562 
665 

767 
870 
972 

073 
175 
276 

469 
572 
675 

778 
880 
982 

083 

185 
286 

480 
583 

685 

788 
890 
992 

094 
195 
296 

490 
593 
696 

798 
900 
*002 

104 
205 
306 

500 
603 
706 

808 
910 
*012 

114 
215 
317 

511 
613 
716 

818 
921 
*022 

124 
225 
327 

521 
624 
726 

829 
931 
*033 

134 
236 
337 

430 

347 

357 

367 

377 

387 

397 

407 

417 

428 

438 

431 
432 
433 

434 
435 
436 

437 
438 
439 

448 
548 
649 

749 
849 
949 

64048 
147 
246 

458 
558 
659 

759 

859 
959 

058 
157 
256 

468 
568 
669 

769 
869 
969 

068 
167 
266 

478 
579 
679 

779 
879 
979 

078 
177 
276 

488 
689 
689 

789 
889 
988 

088 
187 
286 

498 
599 
699 

799 
899 
998 

098 
197 
296 

508 
609 
709 

809 
909 

*008 

108 
207 
306 

518 
619 
719 

819 
919 
*018 

118 

217 
316 

528 
629 
729 

829 
929 
*028 

128 
227 
326 

538 
639 
739 

839 
939 
*038 

137 

237 
335 

440 

345 

355 

365 

375 

385 

395 

404 

414 

424 

434 

441 
442 
443 

444 
445 
446 

447 
448 
449 

444 
542 
640 

738 
836 
933 

65031 
128 
225 

454 
552 
650 

748 
846 
943 

040 
137 
234 

464 
562 
660 

758 
856 
953 

050 
147 
244 

473 
572 
670 

768 
865 
963 

060 
157 

254 

483 
582 
680 

777 
875 
972 

070 
167 
263 

493 
591 
689 

787 
885 
982 

079 
176 
273 

503 
601 
699 

797 
895 
992 

089 
186 
283 

513 
611 
709 

807 
904 
*002 

099 
196 
292 

523 
621 
719 

816 
914 
*011 

108 
205 
302 

532 
631 
729 

826 
924 
*021 

118 
215 
312 

450 

321 

331 

341 

350 

360 

369 

379 

389 

398 

408 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop.  Pts. 

I] 


450  —  Logarithms  of  Numbers  —  500 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop.  Pts. 

450 

65321 

331 

341 

350 

360 

369 

379 

389 

398 

408 

451 

418 

427 

437 

447 

456 

466 

475 

485 

495 

504 

452 

514 

523 

533 

543 

552 

562 

571 

581 

591 

600 

453 

610 

619 

629 

639 

648 

658 

667 

677 

686 

696 

454 

706 

715 

725 

734 

744 

753 

763 

772 

782 

792 

455 

801 

811 

820 

830 

839 

849 

858 

868 

877 

887 

456 

896 

906 

916 

925 

935 

944 

954 

963 

973 

982 

457 

992 

*001 

*011 

*020 

*030 

*039 

*049 

*058 

*068 

*077 

458 

66087 

096 

106 

115 

124 

134 

143 

153 

162 

172 

459 

181 

191 

200 

210 

219 

229 

238 

247 

257 

266 

460 

276 

285 

295 

304 

314 

323 

332 

342 

351 

361 

mA  '  1 

461 
462 

370 
464 

380 
474 

389 
483 

398 
492 

408 
502 

417 
511 

427 
521 

436 
630 

445 
539 

455 
549 

10 

1  1.0 

&. 

463 

658 

567 

577 

586 

596 

605 

614 

624 

633 

642 

2  2.0 

464 

652 

661 

671 

680 

689 

699 

708 

717 

727 

736 

T'  3.0 

2?F 

465 

745 

755 

764 

773 

783 

792 

801 

811 

820 

829 

4  4.0 

3.6 

466 

839 

848 

857 

867 

876 

885 

894 

904 

913 

922 

5  5.0 

4.5 

6  6.0 

5.4 

467 

932 

941 

950 

960 

969 

978 

987 

997 

*006 

*015 

7  7.0 

6.3 

468 

67025 

034 

043 

052 

062 

071 

080 

089 

099 

108 

8  8.0 

7.2 

469 

117 

127 

136 

145 

154 

164 

173 

182 

191 

201 

9  9.0 

8.1 

470 

210 

219 

228 

237 

247 

256 

265 

274 

284 

293 

471 

302 

311 

321 

330 

339 

348 

357 

367 

376 

385 

472 

394 

4P3 

413 

422 

431 

440 

449 

459 

468 

477 

473 

486 

495 

504 

514 

523 

532 

541 

550 

560 

569 

474 

578 

587 

596 

605 

614 

624 

633 

642 

651 

660 

475 

669 

679 

688 

697 

706 

715 

724 

733 

742 

752 

476 

761 

770 

779 

788 

797 

806 

815 

825 

834 

843 

477 

852 

861 

870 

879 

888 

897 

906 

916 

925 

934 

478 

943 

952 

961 

970 

979 

988 

997 

*006 

*015 

*024 

479 

68034 

043 

052 

061 

070 

079 

088 

097 

106 

115 

480 

124 

133 

142 

151 

160 

169 

178 

187 

196 

205 

481 

215 

224 

233 

242 

251 

260 

269 

278 

287 

296 

8 

482 

305 

314 

323 

332 

341 

350 

359 

368 

377 

386 

1  0.8 

483 

395 

404 

413 

422 

431 

440 

449 

458 

467 

476 

2  1. 

6 

484 

485 

494 

502 

511 

520 

629 

538 

547 

556 

565 

3  2.4 

485 

574 

583 

592 

601 

610 

619 

628 

637 

646 

655 

4  3. 

2 

486 

664 

673 

681 

690 

699 

708 

717 

726 

735 

744 

540 

6  4. 

S 

487 

753 

762 

771 

780 

789 

797 

806 

815 

824 

833 

7  5.6 

488 

842 

851 

860 

869 

878 

886 

895 

904 

913 

922 

8  6.4 

489 

931 

940 

949 

958 

966 

975 

984 

993 

*002 

*011 

9  72 

490 

69020 

028 

037 

046 

055 

064 

073 

082 

090 

099 

491 

108 

117 

126 

135 

144 

152 

161 

170 

179 

188 

492 

197 

205 

214 

223 

232 

241 

249 

258 

267 

276 

493 

285 

294 

302 

311 

320 

329 

338 

346 

355 

364 

494 

373 

381 

390 

399 

408 

417 

425 

434 

443 

452 

495 

461 

469 

478 

487 

496 

504 

513 

522 

531 

539 

496 

548 

557 

566 

574 

583 

592 

601 

609 

618 

627 

497 

636 

644 

653 

662 

671 

679 

688 

697 

705 

714 

498 

723 

732 

740 

749 

758 

767 

775 

784 

793 

801 

499 

810 

819 

827 

836 

845 

854 

862 

871 

880 

888 

500 

897 

906 

914 

923 

932 

940 

949 

958 

966 

975 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop.  Pts. 

10 


500  —  Logarithms  of  Numbers  —  550 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop.  Pts. 

500 

69897 

906 

914 

923 

932 

940 

949 

958 

966 

975 

log  5 
=.69897  00043 

9   8 

1  0.9  0.8 
2  1.8  1.6 
3  2.7  2.4  . 
4  3.6  3.2' 
5  4.5  4.0 
6  5.4  4.8 
7  6.3  5.6 
8  7.2  6.4 
9  8.1  7.2 

7 

1  0.7 
2  1.4 
3  2.1 
4  2.8 
6  3.5 
6  4.2 
7  4.9 
8  5.6 
9  6.3 

501 
502 
503 

504 
505 
506 

507 

508 
509 

984 
70070 
157 

243 
329 
415 

501 
586 
672 

992 
079 
165 

252 
338 
424 

509 
595 
680 

*001 
088 
174 

260 
346 
432 

618 
603 
689 

*010 
096 
183 

269 
355 
441 

526 
612 

697 

*018 
105 
191 

278 
364 
449 

535 
621 

706 

*027 
114 
200 

286 
372 
458 

544 
629 
714 

*036 
122 
209 

295 
381 
467 

552 
638 

723 

*044 
131 
217 

303 
389 
475 

561 
646 
731 

*053 
140 
226 

312 

398 
484 

569 
655 
740 

*062 
148 
234 

321 
406 
492 

678 
663 
749 

510 

757 

766 

774 

783 

791 

800 

808 

817 

825 

834 

511 
512 
513 

514 
515 
516 

517 
518 
519 

842 
927 
71012 

096 
181 
265 

349 
433 

517 

851 
935 
020 

105 
189 
273 

357 

441 
525 

859 
944 
029 

113 

198 
282 

366 
450 
633 

868 
952 
037 

122 
206 
290 

374 
458 
542 

876 
961 
046 

130 

214 
299 

383 
466 
550 

885 
969 
054 

139 
223 
307 

391 
475 
559 

893 
978 
063 

147 
231 
315 

399 
483 
567 

902 
986 
071 

155 
240 
324 

408 
492 
575 

910 
995 
079 

164 

248 
332 

416 

500 

584 

919 
*003 
088 

172 

257 
341 

425 

508 
592 

520 

600 

609 

617 

625 

634 

642 

650 

659 

667 

675 

521 
522 
523 

524 
525 
526 

527 
528 
529 

684 
767 
850 

933 
72016 
099 

181 
263 
346 

692 
775 
858 

941 
024 
107 

189 
272 
354 

700 
784 
867 

950 
032 
115 

198 
280 
362 

709 
792 
875 

958 
041 
123 

206 

288 

717 
800 
883 

966 
049 
132 

214 

296 
378 

725 
809 
892 

975 
057 
140 

222 
304 
387 

734 
817 
900 

983 
066 
148 

230 
313 
395 

742 
825 
908 

991 
074 
156 

239 
321 
403 

750 
834 
917 

999 
082 
165 

247 
329 
411 

759 
842 
925 

*008 
090 
173 

255 

337 
419 

370' 

530 

428 

436 

444 

452 

460 

469 

477 

485 

493 

501 

531 
532 
533 

534 
535 
636 

537 
538 
539 

509 
591 
673 

754 
835 
916 

997 
73078 
159 

518 
599 
681 

762 
843 
925 

*006 
086 
167 

526 
607 
689 

770 
852 
933 

*014 
094 
175 

534 
616 
697 

779 
860 
941 

*022 
102 
183 

542 
624 
705 

787 
868 
949 

*030 
111 
191 

550 
632 
713 

795 
876 
957 

*038 

•4A?»- 

558 
640 
722 

803 
884 
965 

*046 
127 
207 

567 
648 
730 

811 
892 
973 

*054 
135 
215 

575 
656 
738 

819 
900 
981 

*062 
143 
223 

583 
665 
746 

827 
908 
989 

*070 
151 
231 

ISST 

540 

239 

247 

255 

263 

272 

280 

288 

296 

304 

312 

541 
542 
543 

544 
545 
546 

547 
548 
549 

320 
400 
480 

560 
640 
719 

799 

878 
957 

328 
408 
488 

668 
648 

727 

807 
886 
965 

336 
416 
496 

576 
656 
735 

815 
894 
973 

344 
424 
504 

584 
664 
743 

823 
902 
981 

352 
432 
512 

592 
672 
751 

830 
910 
989 

360 
440 
520 

600 
679 
759 

838 
918 
997 

368 

448 
528 

608 
687 
767 

846 
926 
*005 

376 
456 
536 

616 
695 
775 

854 
933 
*013 

384 
464 
544 

624 
703 
783 

862 
941 
*020 

392 
472 
552 

632 
711 
791 

870 
949 
*028 

550 

74036 

044 

052 

060 

068 

076 

084 

092 

099 

107 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop.  Pts. 

550  —  Logarithms  of  Numbers  —  600 


11 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop.  Pts. 

550 

74036 

044 

052 

060 

068 

076 

084 

092 

099 

107 

551 

115 

123 

131 

139 

147 

155 

162 

170 

178 

186 

552 

194 

202 

210 

218 

225 

233 

241 

249 

257 

265 

553 

273 

280 

288 

296 

304 

312 

320 

327 

335 

343 

554 

351 

359 

367 

374 

382 

390 

398 

406 

414 

421 

555 

429 

437 

445 

453 

461 

468 

476 

484 

492 

500 

556 

507 

515 

523 

531 

539 

547 

554 

562 

570 

578 

557 

586 

593 

601 

609 

617 

624 

632 

640 

648 

656 

558 
559 

663 
741 

671 

749 

679 
757 

687 

7G4 

m 

.702 
780 

710 

788 

718 
796 

726 
803 

733 
811 

560 

819 

827 

834 

842 

850 

858 

865 

873 

881 

889 

561 

896 

904 

912 

920 

927 

935 

943 

950 

958 

966 

562 

974 

981 

989 

997 

*005 

*012 

*020 

*028 

*035 

*043 

563 

75051 

059 

066 

074 

082 

089 

097 

105 

113 

120 

564 

128 

136 

143 

151 

159 

166 

174 

182 

189 

197 

565 

205 

213 

220 

228 

236 

243 

251 

259 

266 

274 

566 

282 

289 

297 

305 

312 

320 

328 

335 

343 

351 

567 

358 

366 

374 

381 

389 

397 

404 

412 

420 

427 

568 

435 

442 

450. 

458 

465 

473 

481 

488 

496 

504 

569 

511 

519 

5%L 

534 

542 

549 

557 

565 

572 

580 

570 

587 

595 

603 

610° 

,618 

626 

633 

641 

648 

656 

8mm 

571 

664 

671 

679 

686 

694 

702 

709 

717 

724 

732 

7 

572 

740 

747 

755 

762 

770 

778 

785 

793 

800 

808 

1  0.8  0.7 

573 

815 

823 

831 

838 

846 

853 

861 

868 

876 

884 

2  1.6  1.4 

574 

891 

899 

906 

914 

921 

929 

937 

944 

952 

959 

3  2.4  2.1 

575 

967 

974 

982 

989 

997 

*005 

*012 

*020 

*027 

*035 

4  3.2  2.8 

5   A  f\   OK 

576 

76042 

050 

057 

065 

072 

080 

087 

095 

103 

110 

4.U  o.o 

6  4.8  4.2 

577 

118 

125 

133 

140 

148 

155 

163 

170 

178 

185 

7  5.6  4.9 

578 

193 

200 

208 

215 

223 

230 

238 

245 

253 

260 

8  6.4  5.6 

579 

268 

275 

283 

290 

298 

305 

313 

320 

328 

335 

9  7.2  6.3 

580 

343 

350 

358 

365 

373 

380 

388 

395 

403 

410 

581 

418 

425 

433 

440 

448 

455 

462 

470 

477 

485 

582 

492 

500 

507 

515 

522 

530 

537 

545 

552 

559 

583 

567 

574 

582 

589 

597 

604 

612 

619 

626 

634 

584 

641 

649 

656 

664 

671 

678 

686 

693 

701 

708 

585 

716 

723 

730 

738 

745 

753 

760 

768 

775 

782 

586 

790 

797 

805 

812 

819 

827 

834 

842 

849 

856 

587 

864 

871 

879 

886 

893 

901 

908 

916 

923 

930 

588 

938 

945 

953 

960 

967 

975 

982 

989 

997 

*004 

589 

77012 

019 

026 

034 

041 

048 

056 

063 

070 

078 

590 

085 

093 

100 

107 

115 

122 

129 

137 

144 

151 

591 

159 

166 

173 

181 

188 

195 

203 

210 

217 

225 

592 

232 

240 

247 

254 

262 

269 

276 

283 

291 

298 

593 

305 

313 

320 

327 

335 

342 

349 

357 

364 

371 

594 

379 

386 

393 

401 

408 

415 

422 

430 

437 

444 

595 

452 

459 

466 

474 

481 

488 

495 

503 

510 

517 

596 

525 

532 

539 

546 

554 

561 

568 

576 

583 

590 

597 

597 

605 

612 

619 

627 

634 

641 

648 

656 

663 

598 

670 

677 

685 

692 

699 

706 

714 

721 

728 

735 

599 

743 

750 

757 

764 

772 

779 

786 

793 

801 

808 

600 

815 

822 

830 

837 

844 

851 

859 

866 

873 

880 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop.  Pts. 

12 


600  —  Logarithms  of  Numbers  —  650 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop.  Pts. 

600 

77815 

822 

830 

837 

844 

851 

859 

866 

873 

880 

601 

887 

895 

902 

909 

916 

924 

931 

938 

945 

952 

602 

960 

967 

974 

981 

988 

996 

*003 

*010 

*017 

*025 

603 

78032 

039 

046 

053 

061 

068 

075 

082 

089 

097 

604 

104 

111 

118 

125 

132 

140 

147 

154 

161 

168 

605 

176 

183 

190 

197 

204 

211 

219 

226 

233 

240 

606 

247 

254 

262 

269 

276 

283 

290 

297 

305 

312 

607 

319 

326 

333 

340 

347 

355 

362 

369 

376 

383 

608 

390 

398 

405 

412 

419 

426 

433 

440 

447 

455 

609 

462 

469 

476 

483 

490 

497 

504 

512 

519 

526 

610 

533 

540 

547 

554 

561 

569 

576 

583 

590 

597 

8fm 

611 

604 

611 

618 

625 

633 

640 

647 

654 

661 

668 

7 

612 

675 

682 

689 

696 

704 

711 

718 

725 

732 

739 

I  0.8  0.7 

613 

746- 

753 

760 

767 

774 

781 

789 

796 

803 

810 

2  1.6  1.4 

614 

817 

824 

831 

838 

845 

852 

859 

866 

873 

880 

3  2.4  2.1 

615 

888 

895 

902 

909 

916 

923 

930 

937 

944 

951 

4  3.2  2.8 

616 

958 

965 

972 

979 

986 

993 

*000 

*007 

*014 

*021 

5  4.0  3.5 
6  4.8  4.2 

617 

79029 

036 

043 

050 

057 

064 

071 

078 

085 

092 

7  5.6  4.9 

618 

099 

106 

113 

120 

127 

134 

141 

148 

155 

162 

8  6.4  5.6 

619 

169 

176 

183 

190 

197 

204 

211 

218 

225 

232 

9  7.2  6.3 

620 

239 

246 

253 

260 

267 

274 

281 

288 

295 

302 

621 

309 

316 

323 

330 

337 

344 

351 

358 

365 

372 

622 

379 

386 

393 

400 

407 

414 

421 

428 

435 

442 

623 

449 

456 

463 

470 

477 

484 

491 

498 

505 

511 

624 

518 

525 

532 

539 

546 

553 

560 

567 

574 

581 

625 

588 

595 

602 

609 

616 

623 

630 

637 

644 

650 

626 

657 

664 

671 

678 

685 

692 

699 

706 

713 

720 

627 

727 

734 

741 

748 

754 

761 

768 

775 

782 

789 

628 

796 

803 

810 

817 

824 

831 

837 

844 

851 

858 

629 

865 

872 

879 

886 

893 

900 

906 

913 

920 

927 

630 

934 

941 

948 

955 

962 

969 

975 

982 

989 

996 

631 

80003 

010 

017 

024 

030 

037 

044 

051 

058 

065 

6 

632 

072 

079 

085 

092 

099 

106 

113 

120 

127 

134 

1  0.6 

633 

140 

147 

154 

161 

168 

175 

182 

188 

195 

202 

2  1.2 

634 

209 

216 

223 

229 

236 

243 

250 

257 

264 

271 

3  1.8 

635 

277 

284 

291 

298 

305 

312 

318 

325 

332 

339 

4  2.4 

636 

346 

353 

359 

366 

373 

380 

387 

393 

400 

407 

5  3.0 
6  3.6 

637 

414 

421 

428 

434 

441 

448 

455 

462 

468 

475 

7  4.2 

638 

482 

489 

496 

502 

509 

516 

523 

530 

536 

543 

8  4.8 

639 

550 

557 

564 

570 

577 

584 

591 

598 

604 

611 

9  5.4 

640 

618 

625 

632 

638 

645 

652 

659 

665 

672 

679 

641 

686 

693 

699 

706 

713 

720 

726 

733 

740 

747 

642 

754 

760 

767 

774 

781 

787 

794 

801 

808 

814 

643 

821 

828 

835 

841 

848 

855 

862 

868 

875 

882 

644 

889 

895 

902 

909 

916 

922 

929 

936 

943 

949 

645 

956 

963 

969 

976 

983 

990 

996 

*003 

*010 

*017 

646 

81023 

030 

037 

043 

050 

057 

064 

070 

077 

084 

647 

090 

097 

104 

111 

117 

124 

131 

137 

144 

151 

648 

158 

164 

171 

178 

184 

191 

198 

204 

211 

218 

649 

224 

231 

238 

245 

251 

258 

265 

271 

278 

285 

650 

291 

298 

305 

311 

318 

325 

331 

338 

345 

351 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop.  Pts. 

I] 


650  —  Logarithms  of  Numbers  —  700 


13 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop.  Pts. 

650 

81291 

298 

305 

311 

318 

325 

331 

338 

345 

351 

651 

358 

365 

371 

378 

385 

391 

398 

405 

411 

418 

652 

425 

431 

438 

445 

451 

458 

465 

471 

478 

485 

653 

491 

498 

505 

511 

518 

525 

531 

538 

544 

551 

654 

558 

564 

571 

578 

584 

591 

598 

604 

611 

617 

655 

624 

631 

637 

644 

651 

657 

664 

671 

677 

684 

656 

690 

697 

704 

710 

717 

723 

730 

737 

743 

750 

657 

757 

763 

770 

776 

783 

790 

796 

803 

809 

816 

658 

823 

829 

836 

842 

849 

856 

862 

869 

875 

882 

659 

889 

895 

902 

908 

915 

921 

928 

935 

941 

948 

660 

954 

961 

968 

974 

981 

987 

994 

*000 

*007 

*014 

661 

82020 

027 

033 

040 

046 

053 

060 

066 

073 

079 

662 

086 

092 

099 

-105 

112 

119 

125 

132 

138 

145 

663 

151 

158 

164 

171 

178 

184 

191 

197 

204 

210 

664 

217 

223 

230 

236 

243 

249 

256 

263 

269 

276 

665 

282 

289 

295 

302 

308 

315 

321 

328 

334 

341 

666 

347 

354 

360 

367 

373 

380 

387 

393 

400 

406 

667 

413 

419 

426 

432 

439 

445 

452 

458 

465 

471 

668 

478 

484 

491 

497 

504 

510 

517 

523 

530 

536 

669 

543 

549 

556 

562 

569 

575 

582 

588 

595 

601 

670 

607 

614 

620 

627 

633 

640 

646 

653 

659 

666, 

671 

672 

679 

685 

692 

698 

705 

711 

718 

724 

730 

T  6 

672 

737 

743 

750 

756 

763 

769 

776 

782 

789 

795 

1  0.7  0.6 

673 

802 

808 

814 

821 

827 

834 

840 

847 

853 

860 

2  1.4  1.2 

674 

866 

872 

879 

885 

892 

898 

905 

911 

918 

924 

3  2.1  1.8 

675 

930 

937 

943 

950 

956 

963 

969 

975 

982 

988 

4  2.8  2.4 

676 

995 

*001 

*008 

*014 

*020 

*027 

*033 

*040 

*046 

*052 

5  3.5  3.0 

6  4.2  3.6 

677 

83059 

065 

072 

078 

085 

091 

097 

104 

110 

117 

7  4.9  4.2 

678 

123 

129 

136 

142 

149 

155 

161 

168 

174 

181 

8  5.6  4.8 

679 

187 

193 

200 

206 

213 

219 

225 

232 

238 

245 

9  6.3  5.4 

680 

251 

257 

264 

270 

276 

283 

289 

296 

302 

308 

681 

315 

321 

327 

334 

340 

347 

353 

359 

366 

372 

682 

378 

385 

391 

398 

404 

410 

417 

423 

429 

436 

683 

442 

448 

455 

461 

467 

474 

480 

487 

493 

499 

684 

506 

512 

518 

525 

531 

537 

544 

550 

556f 

563 

685 

569 

575 

582 

588 

594 

601 

607 

613 

620' 

626 

686 

632 

639 

645 

651 

658 

664 

670 

677 

683 

689 

687 

696 

702 

708 

715 

721 

727 

734 

740 

746 

753 

688 

759 

765 

771 

778 

784 

790 

797 

803 

809 

816 

689 

822 

828 

835 

841 

847 

853 

860 

866 

872 

879 

690 

885 

891 

897 

904 

910 

916 

923 

929 

935 

~942~ 

691 

948 

954 

960 

967 

973 

979 

985 

992 

998 

*004 

692 

84011 

017 

023 

029 

036 

042 

048 

055 

061 

067 

693 

073 

080 

086 

092 

098 

105 

111 

117 

123 

130 

694 

136 

142 

148 

155 

161 

167 

173 

180 

186 

192 

695 

198 

205 

211 

217 

223 

230 

236 

242 

248 

255 

696 

261 

267 

273 

280 

286 

292 

298 

305 

311 

317 

697 

323 

330 

336 

-342 

348 

354 

361 

367 

373 

379 

698 

386 

392 

398 

404 

410 

417 

423 

429 

435 

442 

699 

448 

454 

460 

466 

473 

479 

485 

491 

497 

504 

700 

510 

516 

522 

528 

535 

541 

547 

553 

559 

566 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop.  Pts. 

14 


700  —  Logarithms  of  Numbers  —  750 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop.  Pts. 

700 

84510 

516 

522 

528 

535 

541 

547 

553 

559 

566 

log  7 
=.8450£ 

7 

1  0.7 
2  1.4 
3  2.1 

4  2.8 
5  3.5 
6  4.2 
7  4.S 
8  5.6 
9  6.3 

1 
2 
3 
4 
5 
6 
7 
8 
9 

80400 

j 

0.6 
1.2 
1.8 
2.4 
3.0 
3.6 
4.2 
4.8 
5.4 

6 

3.6 
1.0 
1.5 
2.0 
2.5 
3.0 
3.5 
4.0 
1.5 

701 
702 
703 

704 
705 
706 

707 
708 
709 

672 
634 
696 

757 
819 
880 

942 
85003 
065 

578 
640 
702 

763 
825 

887 

948 
009 
071 

584 
646 
708 

770 
831 
893 

954 
016 
077 

590 
652 
714 

776 
837 
899 

960 
022 
083 

597 
658 
720 

782 
844 
905 

967 
028 
089 

603 
665 

726 

788 
850 
911 

973 
034 
095 

609 
671 
733 

794 
856 
917 

979 
040 
101 

615 
677 
739 

800 
862 
924 

985 
046 
107 

621 
683 
745 

807 
868 
930 

991 
052 
114 

628 
689 
751 

813 
874 
936 

997 
058 
120 

710 

126 

132 

138 

144 

150 

156 

163 

169 

175 

181 

711 
712 

713 

714 
715 
716 

717 
718 
719 

187 
248 
309 

370 
431 
491 

552 
612 
673 

193 
254 
315 

376 
437 
497 

558 
618 
679 

199 
260 
321 

382 
443 
503 

564 
625 
685 

205 
266 
327 

388 
449 
509 

570 
631 
691 

211 
272 
333 

394 
455 
516 

576 
637 
697 

217 
278 
339 

400 
461 
522 

582 
643 
703 

224 
285 
345 

406 
467 

528 

688 
649 
709 

230 
291 
352 

412 
473 
534 

594 

655 
715 

236 
297 
358 

418 
479 
540 

600 
661 
721 

242 
303 
364 

425 

485 
546 

606 
667 

727 

720 

733 

739 

745 

751 

757 

763 

769 

775 

781 

788 

721 
722 
723 

724 
725 
726 

727 

728 
729 

794 
854 
914 

974 
86034 
094 

153 
213 
273 

800 
860 
920 

980 
040 
100 

159 
219 
279 

806 
866 
926 

986 
046 
106 

165 

225 
285 

812 
872 
932 

992 
052 
112 

171 
231 
291 

818 
878 
938 

998 
058 
118 

177 
237 
297 

824 
884 
944 

*004 
064 
124 

183 
243 
303 

830 
890 
950 

*010 
070 
130 

189 
249 
308 

836 
896 
956 

*016 
076 
136 

195 
255 
314 

842 
902 
962 

*022 
082 
141 

201 
261 
320 

848 
908 
968 

*028 
088 
147 

207 
267 
326 

730 

332 

338 

344 

350 

356 

362 

368 

374 

380 

386 

731 
732 
733 

734 
735 
736 

737 

738 
739 

392 
451 
610 

670 
629 
688 

747 
806 
864 

398 
457 
516 

576 
635 
694 

753 
812 
870 

404 
~4E3 
522 

581 
641 
700 

759 
817 
876 

410 
469 
528 

587 
646 
705 

764 
823 

882 

415 
475 
534 

593 
652 
711 

770 
829 

888 

421 
481 
540 

599 
658 
717 

776 
835 
894 

427 
487 
546 

605 
664 
723 

782 
841 
900 

433 
493 
552 

611 
670 

729 

788 
847 
906 

439 
499 
558 

617 
676 
735 

794 
853 
911 

445 
504 
564 

623 
682 

74J 

800 
859 
917 

740 

923 

929 

935 

941 

947 

953 

958 

964 

970 

976 

741 

742 
743 

744 
745 
746 

747 
748 
749 

982 
87040 
099 

157 

216 
274 

332 
390 

448 

988 
046 
105 

163 
221 
280 

338 
396 

454 

994 
052 
111 

169 

227 
286 

344 
402 
460 

999 
058 
116 

175 
233 
291 

349 

408 
466 

*005 
064 
122 

181 
239 
297 

355 
413 
471 

*011 
070 
128 

186 
245 
303 

361 
419 

477 

*017 
075 
134 

192 
251 
309 

367 
425 
483 

*023 
081 
140 

198 
256 
315 

373 
431 

489 

*029 
087 
146 

204 
262 
320 

379 
437 
495 

*035 
093 
151 

210 
268 
326 

384 
442 
500 

750 

506 

512 

518 

523 

529 

535 

541 

547 

552 

558 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop.  Pts. 

I] 


750  —  Logarithms  of  Numbers  —  800 


15 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop.  Pts. 

750 

87506 

512 

518 

523 

529 

535 

541 

547 

552 

558 

6   5 

1  0.6  0.5 
2  1.2  1.0 
3  1.8  1.5 
4  2.4  2.0 
5  3.0  2.5 
6  3.6  3.0 
7  4.2  3.5 
8  4.8  4.0 
9  5.4  4.5 

751 
752 
753 

754 
755 
756 

757 
758 
759 

564 
622 
679 

737 

795 
852 

910 
967 
88024 

570 
628 
685 

743 
800 

858 

915 

973 
030 

576 
633 
691 

749 
806 
864 

921 
978 
036 

581 
639 
697 

754 
812 
869 

927 
984 
041 

587 
645 
703 

760 
818 
875 

933 
990 
047 

593 
651 

708 

766 
823 

881 

938 
996 
053 

599 
656 
714 

772 
829 

887 

944 
*001 
058 

604 
662 
720 

777 
835 
892 

950 
*007 
064 

610 
668 
726 

783 
841 
898 

955 
*013 
070 

616 
674 
731 

789 
846 
904 

961 
*018 
076 

760 

081 

087 

093 

098 

104 

110 

116 

121 

127 

133 

761 
762 
763 

764 
765 
766 

767 
768 
769 

138 
195 
252 

309 
366 
423 

480 
536 
593 

144 
201 
258 

315 
372 
429 

485 
542 

598 

150 
207 
264 

321 
377 
434 

491 
547 
604 

156 
213 
270 

(326> 

161 
218 
275 

332 
389 
446 

502 
559 
615 

167 
224 
281 

338 
395 
451 

508 
564 
621 

173 
230 

287 

343 
400 
457 

513 
570 

627 

178 
235 
292 

349 
406 
463 

519 
576 
632 

184 
241 
298 

355 
412 
468 

525 

581 
638 

190 
247 
304 

360 
417 
474 

530 

587 
643 

440 

497 
553 
610 

770 

649 

655 

660 

666 

672 

677 

683 

689 

694 

700 

771 
772 
773 

774 
775 
776 

777 

778 
779 

705 
762 
818 

874 
930 
986 

89042 
098 
154 

711 
767 

824 

880 
936 
992 

048 
104 
159 

717 
773 
829 

885 
941 
997 

053 
109 
165 

722 
779 
835 

891 
947 
*003 

059 
115 
170 

728 
784 
840 

897 
953 
*009 

064 
120 
176 

734 
790 
846 

902 
958 
*014 

070 
126 
182 

739 
795 

852 

908 
964 
*020 

076 
131 

187 

745 
801 
857 

913 
969 
*025 

081 
137 
193 

750 
807 
863 

919 
975 
*031 

087 
143 

198 

756 
812 
868 

925 
981 
*037 

092 
148 
204 

780 

209 

215 

221 

226 

232 

237 

243 

248 

254 

260 

781 
782 
783 

784 
785 
786 

787 
788 
789 

265 
321 
376 

432 

487 
542 

597 
653 

708 

271 
326 
382 

437 
492 
548 

603 
658 
713 

276 
332 
387 

443 
498 
553 

609 
664 
719 

282 
337 
393 

448 
504 
559 

614 

669 
724 

287 
343 
398 

454 
509 
564 

620 
675 
730 

293 
348 
404 

459 
515 
570 

625 

680 
735 

298 
354 
409 

465 
520 
575 

631 

686 
741 

304 
360 
415 

470 
526 
581 

636 
691 
746 

310 
365 
421 

476 
531 
586 

642 
697 
752 

315 
371 
426 

481 
537 
592 

647 
702 
757 

790 

763 

768 

774 

779 

785 

790 

796 

801 

807 

812 

791 
792 
793 

794 
795 
796 

797 
798 
799 

818 
873 
927 

982 
90037 
091 

146 
200 
255 

823 
878 
933 

988 
042 
097 

151 

206 
260 

829 
883 
938 

993 

048 
102 

157 

211 
266 

834 
889 
944 

998 
053 
108 

162 
217 
271 

840 
894 
949 

*004 
059 
113 

168 
222 
276 

845 
900 
955 

*009 

064 
119 

173 

227 

282 

851 
905 
960 

*015 
069 
124 

179 
233 

287 

856 
911 
966 

*020 
075 
129 

184 
238 
293 

862 
916 
971 

*026 
080 
135 

189 
244 

298 

867 
922 
977 

*031 

086 
140 

195 
249 
304 

800 

309 

314 

320 

325 

331 

336 

342 

347 

352 

358 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop.  Pts. 

16 


800  —  Logarithms  of  Numbers  —  850 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop.  Pts. 

800 

90309 

314 

320 

325 

331 

336 

342 

347 

352 

358 

801 

363 

369 

374 

380 

385 

390 

396 

401 

407 

412 

802 

417 

423 

428 

434 

439 

445 

450 

455 

461 

466 

803 

472 

4tff 

482 

488 

493 

499 

504 

509 

515 

520 

804 

526 

53li 

536 

542 

547 

553 

558 

563 

569 

574 

805 

580 

585 

590 

596 

601 

607 

612 

617 

623 

628 

806 

634 

639 

644 

650 

655 

660 

666 

671 

677 

682 

807 

687 

693 

698 

703 

709 

714 

720 

725 

730 

736 

808 

741 

747 

752 

757 

763 

768 

773 

779 

784 

789 

809 

795 

800 

806 

811 

816 

'822 

827 

832 

838 

843 

810 

849 

854 

859 

865 

870 

875 

881 

886 

891 

897 

811 

902 

907 

913 

918 

924 

929 

934 

940 

945 

950 

812 

956 

961 

966 

972 

977 

982 

988 

993 

998 

*004 

813 

91009 

014 

020 

025 

030 

036 

041 

046 

052 

057 

814 

062 

068 

073 

078 

084 

089 

094 

100 

105 

110 

815 

116 

121 

126 

132 

137 

142 

148 

153 

158 

164 

816 

169 

174 

180 

185 

190 

196 

201 

206 

212 

217 

817 

222 

228 

233 

238 

243 

249 

254 

259 

265 

270 

818 

275 

281 

286 

291 

297 

302 

307 

312 

318 

323 

819 

328 

334 

339 

344 

350 

355 

360 

365 

371 

376 

820 

381 

387 

392 

397 

403 

408 

413 

418 

424 

429 

IX 

61   — 

821 

434 

440 

445 

450 

455 

461 

466 

471 

477 

482 

5 

822 

487 

492 

498 

503 

508 

514 

519 

524 

529 

535 

1  0.6  0.5 

823 

540 

545 

551 

556 

561 

566 

572 

577 

582 

587 

2  1.2  1.0 

824 

593 

598 

603 

609 

614 

619 

624 

630 

635 

640 

3  1.8  1.5 

825 

645 

651 

656 

661 

666 

672 

677 

682 

687 

693 

4.  2.4  2.0 

826 

698 

703 

709 

714 

719 

724 

730 

735 

740 

745 

5  3.0  2.5 
6  3.6  3.0 

827 

751 

756 

761 

766 

772 

777 

782 

787 

793 

798 

7  4.2  3.5 

828 

803 

808 

814 

819 

824 

829 

834 

840 

845 

850 

8  4.8  4.0 

829 

855 

861 

866 

871 

876 

882 

887 

892 

897 

903 

9  5.4  4.5 

830 

908 

913 

918 

924 

929 

934 

939 

944 

950 

955 

831 

960 

965 

971 

976 

981 

986 

991 

997 

*002 

*007 

832 

92012 

018 

023 

028 

033 

038 

044 

049 

054 

059 

833 

065 

070 

075 

080 

085 

091 

096 

101 

106 

111 

834 

117 

122 

127 

132 

137 

143 

148 

153 

158 

163 

835 

169 

174 

179 

184 

189 

195 

200 

205 

210 

215 

836 

221 

226 

231 

236 

241 

247 

252 

257 

262 

267 

837 

273 

278 

283 

288 

293 

298 

304 

309 

314 

319 

838 

324 

330 

335 

340 

345 

350 

355 

361 

366 

371 

839 

376 

381 

387 

392 

397 

402 

407 

412 

418 

423 

840 

428 

433 

438 

443 

449 

454 

459 

464 

469 

474 

841 

480 

485 

490 

495 

500 

505 

511 

516 

521 

526 

842 

531 

536 

542 

547 

552 

557 

562 

567 

§J2 

578 

843 

583 

588 

593 

598 

603 

609 

614 

619 

624 

629 

844 

634 

639 

645 

650 

655 

660 

665 

670 

675 

681 

845 

686 

691 

696 

701 

706 

711 

716 

722 

727 

732 

846 

737 

742 

747 

752 

758 

703 

768 

773 

778 

783 

847 

788 

793 

799 

804 

809 

814 

819 

824 

829 

834 

848 

840 

845 

850 

855 

860 

865 

870 

875 

881 

886 

849 

891 

896 

901 

906 

911 

916 

921 

927 

932 

937 

850 

942 

947 

952 

957 

962 

9G7 

973 

978 

983 

988 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop.  Pts. 

850  —  Logarithms  of  Numbers  —  900 


17 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop.  Pts. 

850 

92942 

947 

952 

957 

962 

967 

973 

978 

983 

988 

851 

993 

998 

*003 

*008 

*013 

*018 

*024 

*029 

*034 

*039 

852 

93044 

049 

054 

059 

064 

069 

075 

080 

085 

090 

853 

095 

100 

105 

110 

115 

120 

125 

131 

136 

141 

854 

146 

151 

156 

161 

166 

171 

176 

181 

186 

192 

855 

197 

202 

207 

212 

217 

222 

227 

232 

237 

242 

856 

247 

252 

258 

263 

268 

273 

278 

283 

288 

293 

857 

298 

303 

308 

313 

318 

323 

328 

334 

339 

344 

858 

349 

354 

359 

364' 

369 

374 

379 

384 

389 

394 

859 

399 

404 

409 

414 

420 

425 

430 

435 

440 

445 

860 

450 

455 

460 

465 

470 

475 

480 

485 

490 

495 

6C  " 

861 

500 

505 

510 

515 

520 

526 

531 

536 

541 

546 

5 

862 

551 

556 

561 

566 

571 

576 

581 

586 

591 

596 

1  0.6  0.5 

863 

601 

606 

611 

616 

621 

626 

63  !., 

636 

641 

646 

2  1.2  1.0 

864 

651 

656 

661 

666 

671 

676 

682 

687 

692 

697 

3  1.8  1.5 

49  A  9  H 

865 

702 

707 

712 

717 

722 

727 

732 

737 

742 

747 

•-.T:   £it\J 

c  ^09^ 

866 

752 

757 

762 

767 

772 

777 

782 

787 

792 

797 

cl   O*U   —  .>> 

6  3.6  3.0 

867 

802 

807 

812 

817 

822 

827 

832 

837 

842 

847 

7  4.2  3.5 

868 

852 

857 

862 

867 

872 

877 

882 

887 

892 

897 

8  4.8  4.0 

869 

902 

907 

912 

917 

922 

927 

932 

937 

942 

947 

9  5.4  4.5 

870 

952 

957 

962 

967 

972 

977 

982 

987 

992 

997 

871 

94002 

007 

012 

017 

022 

027 

032 

037 

042 

047 

872 

052 

057 

062 

067 

072 

077 

082 

086 

091 

096 

873 

101 

106 

111 

116 

121 

126 

131 

136 

141 

146 

874 

151 

156 

161 

166 

171 

176 

181 

186 

191 

196 

875 

201 

206 

211 

216 

221 

226 

231 

236 

240 

245 

876 

250 

255 

260 

265 

270 

275 

280 

285 

290 

295 

877 

300 

305 

310 

315 

320 

325 

330 

335 

340 

345 

878 

349 

354 

359 

364 

369 

374 

379 

384 

389 

394 

879 

399 

404 

409 

414 

419 

424 

429 

433 

438 

443 

880 

448 

453 

458 

463 

468 

473 

478 

483 

488 

493 

881 

498 

503 

507 

512 

517 

522 

527 

532 

537 

542 

4 

882 

547 

552 

557 

562 

567 

571 

576 

581 

586 

591 

1  0.4 

883 

596 

601 

606 

611 

616 

621 

626 

630 

'635 

640 

2  0.8 

884 

645 

650 

655 

660 

665 

670 

675 

680 

685 

689 

3  1.2 

885 

694 

699 

704 

709 

714 

719 

724 

729 

734 

738 

4  1.6 
50  n 

886 

743 

748 

753 

758 

763 

768 

773 

778 

783 

787 

Z.U 

6  2.4 

887 

792 

797 

802 

807 

812 

817 

822 

827 

832 

836 

7  2.8 

888 

841 

846 

851 

856 

861 

866 

871 

876 

880 

885 

8  3.2 

889 

890 

895 

900 

905 

910 

915 

919 

924 

929 

934 

9  3.6 

890 

939 

944 

949 

954 

959 

963 

968 

973 

978 

983 

891 

988 

993 

998 

*002 

*007 

*012 

*017 

*022 

*027 

*032 

892 

95036 

041 

046 

051 

056 

061 

066 

071 

075 

080 

893 

085 

090 

095 

100 

105 

109 

114 

119 

124 

129 

894 

134 

139 

143 

148 

153 

158 

163 

168 

173 

177 

895 

182 

187 

192 

197 

202 

207 

211 

216 

221 

226 

896 

231 

236 

240 

245 

250 

255 

260 

265 

270 

274 

897 

279 

284 

289 

294 

299 

303 

308 

313 

318 

323 

898 

328 

332 

337 

342 

347 

352 

357 

361 

366 

371 

899 

376 

381 

386 

390 

395 

400 

405 

410 

415 

419 

900 

424 

429 

434 

439 

444 

448 

453 

458 

463 

468 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop.  Pts. 

18 


900  —  Logarithms  of  Numbers  —  950 


[1 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop.  Pts. 

900 

95424 

429 

434 

439 

444 

448 

453 

458 

463 

468 

5   4 

1  US  0.4 
2  1.0  0.8 
3  1.5  1.2 
4  2.0  1.6 
5  2.5  2.0 
6  3.0  2.4 
7  3.5  2.8 
8  4.0  3.2 
9  4.5  3.6 

901 
902 
903 

904 
905 
906 

907 
908 
909 

472 
521 
569 

617 
665 
713 

761 

809 
856 

477 
525 
574 

622 
•670" 
718 

766 
813 
861 

482 
530 
578 

626 

674 

722 

770 
818 
866 

487 
535 
583 

631 

679 
727 

775 
823 

871 

492 
540 

588 

636 
684 
732 

780 
828 

875 

497 
545 
593 

641 
689 
737 

785 
832 

880 

501 
550 
598 

646 

694 
742 

789 

837 

885 

506 
554 
602 

650 
698 
746 

794 
842 
890 

511 
559 
607 

655 
703 
751 

799 

847 
895 

516 
564 
612 

660 
708 
756 

804 
852 
899 

910 

904 

909 

914 

918 

923 

928 

933 

938 

942 

947 

911 
912 
913 

914 
915 
916 

917 
918 
919 

952 
999 
96047 

095 
142 
190 

237 

284 
332 

957 
*004 
052 

099 
147 
194 

242 
289 
336 

961 
*009 
057 

104 
152 
199 

246 
294 
341 

966 
*014 
061 

109 
156 
204 

251 

298 
346 

971 
*019 
066 

114 

161 
209 

256 
303 
350 

976 
*023 
071 

118 
1"66 
213 

261 
308 
355 

980 
*028 
076 

123 
171 

218 

265 
313 
360 

985 
*033 
080 

128 
175 
223 

270 
317 
365 

990 
*038 
085 

133 
180 
227 

275 
322 
369 

995 
*042 
090 

137 
185 
232 

280 
327 
374 

920 

379 

384 

388 

393 

398 

402 

407 

412 

417 

421 

921 
922 
923 

924 
925 
926 

927 
928 
929 

426 
473 
520 

567 
614 
661 

708 
755 
802 

431 

478 
525 

572 
619 
666 

713 

759 
806 

435 
483 
530 

577 
624 
670 

717 
764 
811 

440 
487 
534 

581 
628 
675 

722 
769 
816 

445 
492 
539 

586 
633 
680 

727 
774 
820 

450 
497 
544 

591 

638 
685 

731 

778 
825 

454 
501 

548 

595 
642 
689 

736 
783 
830 

459 
506 
553 

600 

0.47 

464 
511 

558 

605 
652 
69^ 

745 
792 
839 

468 
515 
562 

609 
656 
703 

750 
797 
844 

654 

741 

788 
834 

930 

848 

853 

858 

862 

867 

872 

876 

881 

886 

890 

931 
932 
933 

934 
935 
936 

937 

938 
939 

895 
942 
988 

97035 
081 
128 

174 

220 
267 

900 
946 
993 

039 
086 
132 

179 
225 
271 

904 
951 
997 

044 
090 
137 

183 
230 
276 

909 
956 
*002 

049 
095 
142 

188 
234 
280 

914 
960 
*007 

053 
100 
146 

192 
239 

285 

918 
965 
*011 

058 
104 
151 

197 
243 
290 

923 
970 
*016 

063 
109 
155 

202 
248 
294 

928 
974 
*021 

067 
114 
160 

206 
253 
299 

932 
979 
*025 

072 
118 
165 

211 
257 
304 

937 
984 
*030 

077 
123 
169 

216 
262 
308 

940 

313 

317 

322 

327 

331 

336 

340 

345 

350 

354 

941 
942 
943 

944 
945 
946 

947 
948 
949 

359 
405 
451 

497 
543 
589 

635 

681 

727 

364 
410 
456 

502 
548 
594 

640 
685 
731 

368 
414 
460 

506 
552 
598 

644 
690 
736 

373 
419 

465 

511 
557 
603 

649 
695 

740 

377 
424 
470 

516 
562 
607 

653 
699 

745 

382 
428 
474 

520 
566 
612 

658 
704 
749 

387 
433 
479 

525 
571 
617 

663 
708 
754 

391 
437 

483 

529 
575 
621 

667 
713 
759 

396 
442 

488 

534 
580 
626 

672 
717 
763 

400 
447 
493 

539 
585 
630 

676 
722 

768 

950 

772 

777 

782 

786 

791 

795 

800 

804 

809 

813 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop.  Pts. 

950  —  Logarithms  of  Numbers  —  1000 


19 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop.  Pts. 

950 

97772 

777 

782 

786 

791 

795 

800 

804 

809 

813 

951 

818 

823 

827 

832 

836 

841 

845 

850 

855 

859 

952 

864 

868 

873 

877 

88^ 

886 

~891 

896 

900 

905 

953 

909 

914 

918 

923 

928 

932 

937 

941 

946 

950 

954 

955 

959 

964 

968 

973 

978 

982 

987 

991 

996 

955 

98000 

005 

009 

014 

019 

023 

028 

032 

037 

041 

956 

046 

050 

055 

059 

064 

068 

073 

078 

082 

087 

957 

091 

096 

100 

105 

109 

114 

118 

123 

127 

132 

958 

137 

141 

146 

150 

155 

159 

164 

168 

173 

177 

959 

182 

186 

191 

195 

200 

204 

209 

214 

218 

223 

960 

227 

232 

236 

241 

245 

250 

254 

259 

263 

268 

961 

272 

277 

281 

286 

290 

295 

299 

304 

308 

313 

962 

318 

322 

327 

331 

336 

340 

345 

349 

354 

358 

963 

363 

367 

372 

376 

381 

385 

390 

394 

399 

403 

964 

408 

412 

417 

421 

426 

430 

435 

439 

444 

448 

965 

453 

457 

462 

466 

471 

475 

480 

484 

489 

493 

966 

498 

502 

507 

511 

516 

620 

525 

529 

534 

538 

967 

543 

547 

552 

556 

561 

565 

570 

574 

579 

583 

968 

588 

592 

597 

601 

605 

610 

614 

619 

623 

628 

969 

632 

637 

641 

646 

650 

655 

659 

664 

668 

673 

970 

677 

682 

686 

691 

695 

700 

704 

709 

713 

717 

5.     A 

971 

722 

726 

731 

735 

740 

744 

749 

753 

758 

762 

4 

972 

767 

771 

776 

780 

784 

789 

793 

798 

802 

807 

1  0.5  0.4 

973 

811 

816 

820 

825 

829 

834 

838 

843 

847 

851 

2  1.0  0.8 

974 

856 

860 

865 

869 

874 

878 

883 

887 

892 

896 

3  1.5  1.2 

490  1  fi 

975 

900 

905 

909 

914 

918 

923 

927 

932 

936 

941 

&»\j   i  ,\> 

5  2.5  2.0 

976 

945 

949 

954 

958 

963 

967 

972 

976 

981 

985 

6  3!o  2!4 

977 

989 

994 

998 

*003 

*007 

*012 

*016 

*021 

*025 

*029 

7  3.5  2.8 

978 

99034 

038 

043 

047 

052 

056 

061 

065 

069 

074 

8  4.0  3.2 

979 

078 

083 

087 

092 

096 

100 

105 

109 

114 

118 

9  4.6  3.6 

980 

123 

127 

131 

136 

140 

145 

149 

154 

158 

162 

981 

167 

171 

176 

180 

185 

189 

193 

198 

202 

207 

982 

211 

216 

220 

224 

229 

233 

238 

242 

247 

251 

983 

255 

260 

264 

269 

273 

277 

282 

286 

291 

295 

984 

300 

304 

308 

313 

317 

322 

326 

330 

335 

339 

985 

344 

348 

352 

357 

361 

366 

370 

374 

379 

383 

986 

388 

392 

396 

401 

405 

410 

414 

419 

423 

427 

987 

432 

436 

441 

445 

449 

454 

458 

463 

467 

471 

988 

476 

480 

484 

489 

493 

498 

502 

506 

511 

515 

989 

520 

524 

528 

533 

537 

542 

546 

550 

555 

559 

990 

564 

568 

572 

577 

681 

585 

590 

594 

599 

603 

991 

607 

612 

616 

621 

625 

629 

634 

638 

642 

647 

992 

651 

656 

660 

664 

669 

673 

677 

682 

686 

691 

993 

695 

699 

704 

708 

712 

717 

721 

726 

730 

734 

994 

739 

743 

747 

752 

756 

760 

765 

769 

774 

778 

995 

782 

787 

791 

795 

800 

804 

808 

813 

817 

822 

996 

826 

830 

835 

839 

843 

848 

852 

856 

861 

865 

997 

870 

874 

878 

883 

887 

891 

896 

900 

904 

909 

998 

913 

917 

922 

926 

930 

935 

939 

944 

948 

952 

999 

957 

961 

965 

970 

974 

978 

983 

987 

991 

996 

1000 

00000 

004 

009 

013 

017 

022 

026 

030 

035 

039 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop.  Pts. 

20    Table  la  —  Condensed  Logarithms  and  Antilogarithms   £1* 

CONDENSED  LOGARITHMS  TO  FIFTEEN  DECIMAL  PLACES 

[The  first  digits  of  n  are  given  in  the  first  row  at  the  top;  the  last  digit  of  n  in 
the  left-hand  column.  The  first  column  of  logarithms  are  those  of  1,  2,  3,  •  •  •,  9. 
The  remaining  columns  give  log  (1  +  x),  where  x  =  (0.1)*  times  1,  2,  •  •  •,  9.] 


First  Digit 

of  n  • 


1. 


1.0 


1.00 


Log  n 


First  Digits 
of  log  n 


.0 


.00 


00000  00000  00000 
30102  99956  63981 
47712  12547  19662 
60205  99913  27962 
69897  00043  36019 
77815  12503  83644 
84509  80400  14257 
90308  99869  91944 
95424  25094  39325 


04139  26851  58225 
07918  12460  47625 
11394  33523  06837 
14612  80356  78238 
17609  12590  55681 
204119982655925 
23044  89213  78274 
25527  25051  03306 
27875  36009  52829 


0432  13737  82643 
08600171761918 
1283  72247  05172 
1703  33392  98780 
21189299069938 
2530  58652  64770 
2938  37776  85210 
3342  37554  86950 
3742  64979  40624 


(continuation) 


1.000 

1.0000 

1.00000 

1.000000 

1.0000000 

1.00000000 

.000 

.0000 

.00000 

.000000 

.0000000 

.00000000 

1 

2 
3 
4 
5 
6 
7 
8 
9 

04  34272  76863 
0868502  11649 
13  02688  05227 
17  36830  58465 
21  70929  72230 
26  04985  47390 
30  38997  84812 
34  72966  85364 
39  06892  49910 

04342923104 
0  86858  02780 
1  30286  39028 
1  73714  31850 
2  17141  81245 
26056887215 
3  03995  49761 
3  47421  68884 
3  90847  44584 

04342  94265 
08685  88095 
1302881491 
17371  74453 
21714  66981 
26057  59074 
30400  50733 
34743  41958 
39086  32748 

0434  29446 
0868  58888 
1302  88325 
1737  17758 
2171  47187 
260576611 
304006031 
3474  35447 
3908  64858 

043  42945 
086  85890 
130  28834 
173  71779 
217  14724 
260  57668 
304  00613 
347  43557 
390  86502 

04  34294 
08  68589 
13  02883 
17  37178 
21  71472 
26  05767 
30  40061 
34  74356 
39  08650 

[For  x  <  .00000001,  log  (1  +  x)  =  x-M,  to  within  3  in  the  17th  place,  where 
M  =  0.43429448  •  •  • .  Hence  the  last  column  gives  multiples  of  M  except  for  the 
decimal  place.  All  the  columns  that  would  follow  have  the  same  significant  digits 
displaced  each  time  one  place.] 


CONDENSED  ANTILOGARITHMS  TO  TEN  DECIMAL  PLACES 

[The  first  digits  of  n  are  given  in  the  first  row  at  the  top;  n  =  (0.1)*  x;  x  =  1,  2, 


3,  •  •  • ,  9  are  given  in  the  left-hand  column, 
second  row  at  the  top.] 


The  first  digits  in  10"  are  given  in  the 


X 

n  =  0.1* 

O.Ola; 

O.OOlx 

O.OOOlx 

(O.I)6* 

(0.1)6z 

(0.1)'* 

10" 

1. 

1.0 

1.00 

1.000 

1.0000 

1.00000 

1 

1.2589254118 

02329  29923 

0230  52381 

023  02850 

02  30261 

0  23026 

02303 

2 

1.58489  31925 

04712  85481 

0461  57903 

046  06231 

04  60528 

0  46052 

04605 

3 

1.99526  23150 

07151  93052 

0693  16689 

069  10142 

06  90799 

0  69078 

06908 

4 

2.51188  64315 

09647  81961 

0925  28861 

092  14583 

09  21076 

0  92104 

09210 

5 

3.16227  76602 

12201  84543 

115794543 

115  19555 

11  51359 

1  15130 

11513 

6 

3.98107  17055 

14815  36215 

1391  13857 

138  25058 

13  81646 

1  38156 

13816 

7 

5.0118723363 

17489  75549 

1624  86929 

161  31092 

16  11939 

1  61182 

16118 

8 

6.30957  34448 

20226  44346 

1859  13881 

184  37657 

18  42238 

1  84209 

18421 

9 

7.94328  23472 

23026  87708 

2093  94837 

207  44753 

20  72541 

2  07235 

20723 

[For  n  <  0.000001, 10"  =  1  +  n-  (l/M)  to  within  3  in  the  12th  decimal  place,  where 
(l/M)  =  2.302585  •  •  •.  Hence  the  last  column  gives  multiples  of  (l/M)  except  for 
the  decimal  place.  All  the  columns  that  would  follow  contain  the  same  significant 
digits  displaced  one  place  for  each  new  column.] 


TABLE  E 


ACTUAL  VALUES 


OF  THE 


TRIGONOMETRIC  FUNCTIONS 


TO 


FIVE  DECIMAL  PLACES 


Trigonometric  Functions 

and  Their  Inverses 
Thus  y  =  sin  x   gives  x  =  arc  sin  y 


22 


0°  —  Values  of  Trigonometric  Functions  — 


[II 


/ 

Sin 

Tan 

Ctn 

Cos 

/ 

Sin 

Tan 

Ctn 

Cos 

0 

.00000 

.00000 



1.0000 

60 

0 

.01745 

.01746 

57.290 

.99985 

60 

1 

029 

029 

3437.7 

000 

59 

1 

774 

775 

56.351 

984 

59 

2 

058 

aa  058 

1718.9 

000 

58 

2 

803 

804 

55.442 

984 

58 

3 

08J- 

)ll  087 

1145.9 

000 

5'. 

3 

832 

833 

54.561 

983 

57 

4 

lie: 

VJ  116 

859.44 

000 

56 

4 

862 

862 

53.709 

983 

56 

5 

.00145- 

Iflbl46 

687.55 

1.0000 

55 

5 

.01891 

.01891 

52.882 

.99982 

55 

6 

175 

175 

572.96 

000 

54 

6 

920 

920 

52.081 

982 

54 

7 

204 

204 

491.11 

000 

53 

7 

949 

949 

51.303 

981 

53 

8 

233 

i  •  2*3 

429.72 

000 

52 

8 

.01978 

.01978 

50.549 

980 

52 

9 

262 

^262 

381.97 

000 

51 

9 

.02007 

.02007 

49.816 

980 

51 

10 

.00291 

>.\)0291 

343.77 

1.0000 

50 

10 

.02036 

.02036 

49.104 

.99979 

50 

11 

320 

320 

312.52 

.99999 

49 

11 

065 

066 

48.412 

979 

49 

12 

349 

349 

286.48 

999 

48 

12 

094 

095 

47.740 

978 

48 

13 

378 

378 

264.44 

999 

47 

13 

123 

124 

47.085 

977 

47 

14 

407 

407 

245.55 

999 

46 

14 

152 

153 

46.449 

977 

46 

15 

.00436 

.00436 

229.18 

.99999 

45 

15 

.02181 

.02182 

45.829 

.99976 

45 

16 

465 

465 

214.86 

999 

44 

16 

211 

211 

45.226 

976 

44 

17 

495 

495 

202.22 

999 

43 

17 

240 

240 

44.639 

975 

43 

18 

524 

524 

190.98 

999 

42 

18 

269 

269 

44.066 

974 

42 

19 

553 

553 

180.93 

998 

41 

19 

298 

298 

43.508 

974 

41 

20 

.00582 

.00582 

171.89 

.99998 

40 

20 

.02327 

.02328 

42.964 

.99973 

40 

21 

611 

611 

163.70 

998 

39 

21 

356 

357 

42.433 

972 

39 

22 

640 

640 

156.26 

998 

38 

22 

385 

386 

41.916 

972 

38 

23 

669 

669 

149.47 

998 

37 

23 

414 

415 

41.411 

971 

37 

24 

698 

698 

143.24 

998 

36 

24 

443 

444 

40.917 

970 

36 

25 

.00727 

.00727 

137.51 

.99997 

35 

25 

.02472 

.02473 

40.436 

.99969 

35 

26 

756 

756 

132.22 

997 

34 

26 

501 

502 

39.965 

969 

34 

27 

785 

785 

127.32 

997 

33 

27 

530 

531 

39.506 

968 

33 

28 

814 

815 

122.77 

997 

32 

28 

560 

560 

39.057 

967 

32 

29 

844 

844 

118.54 

996 

31 

29 

589 

589 

38.618 

966 

31 

30 

.00873 

.00873 

114.59 

.99996 

30 

30 

.02618 

.02619 

38.188 

.99966 

30 

31 

902 

902 

110.89 

996 

29 

31 

647 

648 

37.769 

965 

29 

32 

931 

931 

107.43 

996 

28 

32 

676 

677 

37.358 

964 

28 

33 

960 

960 

104.17 

995 

27 

33 

705 

706 

36.956 

963 

27 

34 

.00989 

.00989 

101.11 

995 

26 

34 

734 

735 

36.563 

963 

26 

35 

.01018 

.01018 

98.218 

.99995 

25 

35 

.02763 

.02764 

36.178 

.99962 

25 

36 

047 

047 

95.489 

995 

24 

36 

792 

793 

35.801 

961 

24 

37 

076 

076 

92.908 

994 

23 

37 

821 

822 

35.431 

960 

23 

38 

105 

105 

90.463 

994 

22 

38 

850 

851 

35.070 

959 

22 

39 

134 

135 

88.144 

994 

21 

39 

879 

881 

34.715 

959 

21 

40 

.01164 

.01164 

85.940 

.99993 

20 

40 

.02908 

.02910 

34.368 

.99958 

20 

41 

193 

193 

83.844 

993 

19 

41 

938 

939 

34.027 

957 

19 

42 

222 

222 

81.847 

993 

18 

42 

967 

968 

33.694 

956 

18 

43 

251 

251 

79.943 

992 

17 

43 

.02996 

.02997 

33.366 

955 

17 

44 

280 

280 

78.126 

992 

16 

44 

.03025 

.03026 

33.045 

954 

16 

45 

.01309 

.01309 

76.390 

.99991 

15 

45 

.03054 

.03055 

32.730 

.99953 

15 

46 

338 

338 

74.729 

991 

14 

46 

083 

084 

32.421 

952 

14 

47 

367 

367 

73.139 

991 

13 

47 

112 

114 

32.118 

952 

13 

48 

396 

396 

71.615 

990 

12 

48 

141 

143 

31.821 

951 

12 

49 

425 

425 

70.153 

990 

11 

49 

170 

172 

31.528 

950 

11 

50 

.01454 

.01455 

68.750 

.99989 

10 

50 

.03199 

.03201 

31.242 

.99949 

10 

51 

483 

484 

67.402 

989 

9 

51 

228 

230 

30.960 

948 

9 

52 

513 

513 

66.105 

989 

8 

52 

257 

259 

30.683 

947 

8 

53 

542 

542 

64.858 

988 

7 

53 

286 

288 

30.412 

946 

7 

54 

571 

571 

63.657 

988 

6 

54 

316 

317 

30.145 

945 

6 

55 

.01600 

.01600 

62.499 

.99987 

5 

55 

.03345 

.03346 

29.882 

.99944 

5 

56 

629 

629 

61.383 

987 

4 

56 

374 

376 

29.624 

943 

4 

57 

658 

658 

60.306 

986 

3 

57 

403 

405 

29.371 

942 

3 

58 

687 

687 

59.266 

986 

2 

58 

432 

434 

29.122 

941 

2 

59 

716 

716 

58.261 

985 

1 

59 

461 

463 

28.877 

940 

1 

60 

.01745 

.01746 

57.290 

.99985 

0 

60 

.03490 

.03492 

28.636 

.99939 

0 

Cos 

Ctn 

Tan 

Sin 

/ 

Cos 

Ctn 

Tan 

Sin 

/ 

89° 


88C 


II] 


2°  —  Values  of  Trigonometric  Functions  —  3e 


/ 

Sin 

Tan 

Ctn 

Cos 

' 

Sin 

Tan 

Ctn 

Cos 

0 

03490 

.03492 

28.636 

.99939 

60 

0 

.05234 

.05241 

19.081 

.99863 

60 

1 

519 

521 

.399 

938 

59 

1 

263 

270 

18.976 

861 

59 

2 

548 

550 

28.166 

937 

58 

2 

292 

299 

.871 

860 

58 

3 

577 

579 

27.937 

936 

57 

3 

321 

328 

.768 

858 

57 

4 

606 

609 

.712 

935 

56 

4 

350 

357 

.666 

857 

56 

5 

03635 

.03638 

27.490 

.99934 

55 

5 

.05379 

.05387 

18.564 

.99855 

55 

6 

664 

667 

.271 

933 

54 

6 

408 

416 

.464 

854 

54 

7 

693 

696 

27.057 

932 

53 

7 

437 

445 

.366 

852 

53 

8 

723 

725 

26.845 

931 

52 

8 

466 

474 

.268 

851 

52 

9 

752 

754 

.637 

930 

51 

9 

495 

503 

.171 

849 

51 

10 

03781 

.03783 

26.432 

.99929 

50 

10 

.05524 

.05533 

18.075 

.99847 

50 

11 

810 

812 

.230 

927 

49 

11 

553 

562 

17.980 

846 

49 

12 

839 

842 

26.031 

926 

48 

12 

582 

591 

.886 

844 

48 

13 

868 

871 

25.835 

925 

47 

13 

611 

620 

.793 

842 

47 

14 

897 

900 

.642 

924 

46 

14 

640 

649 

.702 

841 

46 

15 

.03926 

.03929 

25.452 

.99923 

45 

15 

.05669 

.05678 

17.611 

.99839 

45 

16 

955 

958 

.264 

922 

44 

16 

698 

708 

.521 

838 

44 

17 

.03984 

.03987 

25.080 

921 

43 

17 

727 

737 

.431 

836 

43 

18 

.04013 

.04016 

24.898 

919 

42 

18 

756 

766 

.343 

834 

42 

19 

042 

046 

.719 

918 

41 

19 

785 

795 

.256 

833 

41 

20 

.04071 

.04075 

24.542 

.99917 

40 

20 

.05814 

.05824 

17.169 

.99831 

40 

21 

100 

104 

.368 

916 

39 

21 

844 

854 

17.084 

829 

39 

22 

129 

133 

.196 

915 

38 

22 

873 

883 

16.999 

827 

38 

23 

159 

162 

24.026 

913 

37 

23 

902 

912 

.915 

826 

37 

24 

188 

191 

23.859 

912 

36 

24 

931 

941 

.832 

824 

36 

25 

.04217 

.04220 

23.695 

.99911 

35 

25 

.05960 

.05970 

16.750 

.99822 

35 

26 

246 

250 

.532 

910 

34 

26 

.05989 

.05999 

.668 

821 

34 

27 

275 

279 

.372 

909 

33 

27 

.06018 

.06029 

.587 

819 

33 

28 

304 

308 

.214 

907 

32 

28 

047 

058 

.507 

817 

32 

29 

333 

337 

23.058 

906 

31 

29 

076 

087 

.428 

815 

31 

30 

.04362 

.04366 

22.904 

.99905 

30 

30 

.06105 

.06116 

16.350 

.99813 

30 

31 

391 

395 

.752 

904 

29 

31 

134 

145 

.272 

812 

29 

32 

420 

424 

.602 

902 

28 

32 

163 

-   175 

.195 

810 

28 

33 

449 

454 

.454 

901 

27 

33 

192 

204 

.119 

808 

27 

34 

478 

483 

.308 

900 

26 

34 

221 

233 

16.043 

806 

26 

35 

.04507 

.04512 

22.164 

.99898 

25 

35 

'.002i>lT 

"!06262 

15.969 

.99804 

25 

36 

536 

541 

22.022 

897 

24 

36 

279 

291 

.895 

803 

24 

37 

565 

670 

21.881 

896 

23 

37 

308 

321 

.821 

801 

23 

38 

594 

599 

.743 

894 

22 

38 

337 

350 

.748 

799 

22 

39 

623 

628 

.606 

893 

21 

39 

366 

379 

.676 

797 

21 

40 

.04653 

.04658 

21.470 

.99892 

20 

40 

.06395 

.06408 

15.605 

.99795 

20 

41 

682 

687 

.337 

890 

19 

41 

424 

438 

.534 

793 

19 

42 

711 

716 

.205 

889 

18 

42 

453 

467 

.464 

792 

18 

43 

740 

745 

21.075 

888 

17 

43 

482 

496 

.394 

790 

17 

44 

769 

774 

20.946 

886 

16 

44 

511 

525 

.325 

788 

16 

45 

.04798 

.04803 

20.819 

.99885 

15 

45 

.06540 

.06554 

15.257 

.99786 

15 

46 

827 

833 

.693 

883 

14 

46 

569 

584 

.189 

784 

14 

47 

856 

862 

.569 

882 

13 

47 

598 

613 

.122 

782 

13 

48 

885 

891 

.446 

881 

12 

48 

627 

642 

15.056 

780 

12 

49 

914 

920 

.325 

879 

11 

49 

656 

671 

14.990 

778 

11 

50 

.04943 

.04949 

20.206 

.99878 

10 

50 

.06685 

.06700 

14.924 

.99776 

10 

51 

.04972 

.04978 

20.087 

876 

9 

51 

714 

730 

.860 

774 

9 

52 

.05001 

.05007 

19.970 

875 

8 

52 

743 

759 

.795 

772 

8 

53 

030 

037 

.855 

873 

7 

53 

773 

788 

.732 

770 

7 

54 

059 

066 

.740 

872 

6 

54 

802 

817 

.669 

768 

6 

55 

.05088 

.05095 

19.627 

.99870 

5 

55 

.06831 

.06847 

14.606 

.99766 

5 

56 

117 

124 

.516 

869 

4 

56 

860 

876 

.544 

764 

4 

57 

146 

153 

.405 

867 

3 

57 

889 

905 

.482 

762 

3 

58 

175 

182 

.296 

866 

2 

58 

918 

934 

.421 

76U 

2 

59 

205 

212 

.188 

864 

1 

59 

947 

963 

.361 

758 

1 

60 

.05234 

.05241 

19.081 

.99863 

0 

60 

.06976 

.06993 

14.301 

.99756 

0 

Cos 

Ctn 

Tan 

Sin 

/ 

Cos 

Ctn 

Tan 

Sin 

/ 

87° 


86C 


'24 


4°  —  Values  of  Trigonometric  Functions  —  5C 


[II 


1 

Sin 

Tan 

Ctn 

Cos 

i 

Sin 

Tan 

Ctn 

Cos 

0 

.06976 

.06993 

14.301 

.99756 

60 

0 

.08716 

.08749 

11.430 

.99619 

60 

1 

.07005 

.07022 

.241 

754 

59 

1 

745 

778 

.392 

617 

59 

2 

034 

051 

.182 

752 

58 

2 

774 

807 

.354 

614 

58 

3 

063 

080 

.124 

750 

57 

3 

803 

837 

.316 

612 

57 

4 

092 

110 

.065 

748 

56 

4 

831 

866 

.279 

609 

56 

5 

.07121 

.07139 

14.008 

.99746 

55 

5 

.08860 

.08895 

11.242 

.99607 

55 

6 

150 

168 

13.951 

744 

54 

6 

889 

925 

.205 

604 

54 

7 

179 

197 

.894 

742 

53 

7 

918 

954 

.168 

602 

53 

8 

208 

227 

.838 

740 

52 

8 

947 

.08983 

.132 

599 

52 

9 

237 

256 

.782 

738 

51 

9 

.08976 

.09013 

.095 

596 

51 

10 

.07266 

.07285 

13.727 

.99736 

50 

10 

.09005 

.09042 

11.059 

.99594 

50 

11 

295 

314 

.672 

734 

49 

11 

034 

071 

11.024 

591 

49 

12 

324 

344 

.617 

731 

48 

12 

063 

101 

10.988 

588 

48 

13 

353 

373 

.563 

729 

47 

13 

092 

130 

.953 

586 

47 

14 

382 

402 

.510 

111 

46 

14 

121 

159 

.918 

583 

46 

15 

.07411 

.07431 

13.457 

.99725 

45 

15 

.09150 

.09189 

10.883 

.99580 

45 

16 

440 

461 

.404 

723 

44 

16 

179 

218 

.848 

578 

44 

17 

469 

490 

.352 

721 

43 

17 

208 

247 

.814 

575 

43 

18 

498 

519 

.300 

719 

42 

18 

237 

111 

.780 

572 

42 

19 

527 

548 

.248 

716 

41 

19 

266 

306 

.746 

570 

41 

20 

.07556 

.07578 

13.197 

.99714 

40 

20 

.09295 

.09335 

10.712 

.99567 

40 

21 

585 

607 

.146 

712 

39 

21 

324 

365 

.678 

564 

39 

22 

614 

636 

.096 

710 

38 

22 

353 

394 

.645 

562 

38 

23 

643 

665 

13.046 

708 

37 

23 

382 

423 

.612 

559 

37 

24 

672 

695 

12.996 

705 

36 

24 

411 

453 

.579 

556 

36 

25 

.07701 

.07724 

12.947 

.99703 

35 

25 

.09440 

.09482 

10.546 

.99553 

35 

26 

730 

753 

.898 

701 

34 

26 

469 

511 

.514 

551 

34 

27 

759 

782 

.850 

699 

33 

27 

498 

541 

.481 

548 

33 

28 

788 

812 

.801 

696 

32 

28 

527 

570 

.449 

545 

32 

29 

817 

841 

.754 

694 

31 

29 

556 

600 

.417 

542 

31 

30 

.07846 

.07870 

12.706 

.99692 

30 

30 

.09585 

.09629 

10.385 

.99540 

30 

31 

875 

899 

.659 

689 

29 

31 

614 

658 

.354 

537 

29 

32 

904 

929 

.612 

687 

28 

32 

642 

688 

.322 

534 

28 

33 

933 

958 

.566 

685 

27 

33 

671 

717 

.291 

531 

27 

34 

962 

.07987 

.520 

683 

26 

34 

700 

746 

.260 

528 

26 

35 

.07991 

.08017 

12.474 

.99680 

25 

35 

.09729 

.09776 

10.229 

.99526 

25 

36 

.08020 

046 

.429 

678 

24 

36 

758 

805 

.199 

523 

24 

37 

049 

075 

.384 

676 

23 

37 

787 

834 

.168 

520 

23 

38 

078 

104 

.339 

673 

22 

38 

816 

864 

.138 

517 

22 

39 

107 

134 

.295 

671 

21 

39 

845 

893 

.108 

514 

21 

40 

.08136 

.08163 

12.251 

.99668 

20 

40 

.09874 

.09923 

10.078 

.99511 

20 

41 

165 

192 

.207 

666 

19 

41 

903 

952 

.048 

508 

19 

42 

194 

221 

.163 

664 

18 

42 

932 

.09981 

10.019 

506 

18 

43 

223 

251 

.120 

661 

17 

43 

961 

.10011 

9.9893 

503 

17 

44 

252 

280 

.077 

659 

16 

44 

.09990 

040 

.9601 

500 

16 

45 

.08281 

.08309 

12.035 

.99657 

15 

45 

.10019 

.10069 

9.9310 

.99497 

15 

46 

310 

339 

11.992 

654 

14 

46 

048 

099 

.9021 

494 

14 

47 

339 

368 

.950 

652 

13 

47 

077 

128 

.8734 

491 

13 

48 

368 

397 

.909 

649 

12 

48 

106 

158 

.8448 

488 

12 

49 

397 

427 

.867 

647 

11 

49 

135 

187 

.8164 

485 

11 

50 

.08426 

.08456 

11.826 

.99644 

10 

50 

.10164 

.10216 

9.7882 

.99482 

10 

51 

455 

485 

.785 

642 

9 

51 

192 

246 

.7601 

479 

9 

52 

484 

514 

.745 

639 

8 

52 

221 

275 

.7322 

476 

8 

53 

513 

544 

.705 

637 

7 

53 

250 

305 

.7044 

473 

7 

54 

542 

573 

.664 

635 

6 

54 

279 

334 

.6768 

470 

6 

55 

.08571 

.08602 

11.625 

.99632 

5 

55 

.10308 

.10363 

9.6493 

.99467 

5 

56 

600 

632 

.585 

630 

4 

56 

337 

393 

.6220 

464 

4 

57 

629 

661 

.546 

627 

3 

57 

366 

422 

.5949 

461 

3 

58 

658 

690 

.507 

625 

2 

58 

395 

452 

.5679 

458 

2 

59 

687 

720 

.468 

622 

1 

59 

424 

481 

.5411 

455 

1 

60 

.08716 

.08749 

11.430 

.99619 

0 

60 

.10453 

.10510 

9.5144 

.99452 

0 

Cos 

Ctn 

Tan 

Sin 

' 

Cos 

Ctn 

Tan 

Sin 

/ 

85° 


84C 


II] 


6°  —  Values  of  Trigonometric  Functions  —  T 


25 


/ 

Sin 

Tan 

Ctn 

Cos 

/ 

Sin 

Tan 

Ctn 

Cos 

0 

10453 

.10510 

9.5144 

.99452 

60 

0 

.12187 

.12278 

8.1443 

.99255 

60 

1 

482 

540 

.4878 

449 

59 

1 

216 

308 

.1248 

251 

59 

2 

511 

569 

.4614 

446 

58 

2 

245 

338 

.1054 

248 

58 

3 

540 

599 

.4352 

443 

57 

3 

274 

367 

.0860 

244 

57 

4 

569 

628 

.4090 

440 

56 

4 

302 

397 

.0667 

240 

56 

5 

10597 

.10657 

9.3831 

.99437 

55 

5 

.12331 

.12426 

8.0476 

.99237 

55 

6~ 

626 

687 

.3572 

434 

54 

6 

360 

456 

.0285 

233 

54 

7 

655 

716 

.3315 

431 

53 

7 

389 

485 

8.0095 

230 

53 

8 

684 

746 

.3060 

428 

52 

8 

418 

515 

7.9906 

226 

52 

9 

713 

775 

.2806 

424 

51 

9 

447 

544 

.9718 

222 

51 

10 

10742 

.10805 

9.2553 

.99421 

50 

10 

.12476 

.12574 

7.9530 

.99219 

50 

11 

771 

834 

.2302 

418 

49 

11 

504 

603 

.9344 

215 

49 

12 

800 

863 

.2052 

415 

48 

12 

533 

633 

.9158 

211 

48 

13 

829 

893 

.1803 

412 

47 

13 

562 

662 

.8973 

208 

47 

14 

858 

922 

.1555 

409 

46 

14 

591 

692 

.8789 

204 

46 

15 

.10887 

.10952 

9.1309 

.99406 

45 

15 

.12620 

.12722 

7.8606 

.99200 

45 

16 

916 

.10981 

.1065 

402 

44 

16 

649 

751 

.8424 

197 

44 

17 

945 

.11011 

.0821 

399 

43 

17 

678 

781 

.8243 

193 

43 

18 

.10973 

040 

.0579 

396 

42 

18 

706 

810 

.8062 

189 

42 

19 

.11002 

070 

.0338 

393 

41 

19 

735 

840 

.7882 

186 

41 

20 

.11031 

.11099 

9.0098 

.99390 

40 

20 

.12764 

.12869 

7.7704 

.99182 

40 

21 

060 

128 

8.9860 

386 

39 

21 

793 

899 

.7525 

178 

39 

22 

089 

158 

.9623 

383 

38 

22 

822 

929 

.7348 

175 

38 

23 

118 

187 

.9387 

380 

37 

23 

851 

958 

.7171 

171 

37 

24 

147 

217 

.9152 

377 

36 

24 

880 

.12988 

.6996 

167 

36 

25 

.11176 

.11246 

8.8919 

.99374 

35 

25 

.12908 

.13017 

7.6821 

.99163 

35 

26 

205 

276 

.8686 

370 

34 

26 

937 

047 

.6647 

160 

34 

27 

^-2tt 

305 

.8455 

367 

33 

27 

966 

076 

.6473 

156 

33 

28 

263 

335 

.8225 

364 

32 

28 

.12995 

106 

.6301 

152 

32 

29 

291 

364 

.7996 

360 

31 

29 

.13024 

136 

.6129 

148 

31 

30 

.11320 

.11394 

8.7769 

.99357 

30 

30 

.13053 

.13165 

7.5958 

.99144 

30 

31 

349 

423 

.7542 

354 

29 

31 

081 

195 

.5787 

141 

29 

32 

378 

452 

.7317 

351 

28 

32 

110 

224 

.5618 

137 

28 

33 

407 

482 

.7093 

347 

27 

33 

139 

254 

.5449 

133 

27 

34 

436 

511 

.6870 

344 

26 

34 

168 

284 

.5281 

129 

26 

35 

.11465 

.11541 

8.6648 

.99341 

25 

35 

.13197 

.13313 

7.5113 

.99125 

25 

36 

494 

570 

.6427 

337 

24 

36 

226 

343 

.4947 

122 

24 

37 

523 

600 

.6208 

334 

23 

37 

254 

372 

.4781 

118 

23 

38 

552 

629 

.5989 

331 

22 

38 

283 

402 

.4615 

114 

22 

39 

580 

659 

.5772 

327 

21 

39 

312 

432 

.4451 

110 

21 

40 

.11609 

.11688 

8.5555 

.99324 

20 

40 

.13341 

.13461 

7.4287 

.99106 

20 

41 

638 

718 

.5340 

320 

19 

41 

370 

491 

.4124 

102 

19 

42 

667 

747 

.5126 

317 

18 

42 

399 

521 

.3962 

098 

18 

43 

696 

777 

.4913 

314 

17 

43 

427 

550 

.3800 

094 

17 

44 

725 

806 

.4701 

310 

16 

44 

456 

580 

.3639 

091 

16 

45 

.11754 

.11836 

8.4490 

.99307 

15 

45 

.13485 

.13609 

7.3479 

.99087 

15 

46 

783 

865 

.4280 

303 

14 

46 

514 

639 

.3319 

083 

14 

47 

812 

895 

.4071 

300 

13 

47 

543 

669 

.3160 

079 

13 

48 

840 

924 

.3863 

297 

12 

48 

572 

698 

.3002 

075 

12 

49 

869 

954 

.3656 

293 

11 

49 

600 

728 

.2844 

071 

11 

50 

.11898 

.11983 

8.3450 

.99290 

10 

50 

.13629 

.13758 

7.2687 

.99067 

10 

51 

927 

.12013 

.3245 

286 

9 

51 

658 

787 

.2531 

063 

9 

52 

956 

042 

.3041 

283 

8 

52 

687 

817 

.2375 

059 

8 

53 

.11985 

072 

.2838 

279 

7 

53 

716 

846 

.2220 

055 

7 

54 

.12014 

101 

.2636 

276 

6 

54 

744 

876 

.2066 

051 

6 

55 

.12043 

.12131 

8.2434 

.99272 

5 

55 

.13773 

.13906 

7.1912 

.99047 

5 

56 

071 

160 

.2234 

269 

4 

56 

802 

935 

.1759 

043 

4 

57 

100 

190 

.2035 

265 

3 

57 

831 

965 

.1607 

039 

3 

58 

129 

219 

.1837 

262 

2 

58 

860 

.13995 

.1455 

035 

2 

59 

158 

249 

.1640 

258 

1 

59 

889 

.14024 

.1304 

031 

1 

60 

.12187 

.12278 

8.1443 

.99255 

0 

60 

.13917 

.14054 

7.1154 

.99027 

0 

Cos 

Ctn 

Tan 

Sin 

/ 

Cos 

Ctn 

Tan 

Sin 

i 

83C 


82C 


26 


8°  —  Values  of  Trigonometric  Functions  —  9C 


[II 


/ 

Sin 

Tan 

Ctn 

Cos 

/ 

Sin 

Tan 

Ctn 

Cos 

0 

.13917 

.14054 

7.1154 

.99027 

60 

0 

.15643 

.15838 

6.3138 

.98769 

60 

1 

946 

084 

.1004 

023 

59 

1 

672 

868 

.3019 

764 

59 

2 

.13975 

113 

.0855 

019 

58 

2 

701 

898 

.2901 

760 

58 

3 

.14004 

143 

.0706 

015 

57 

3 

730 

928 

.2783 

755 

57 

4 

033 

173 

.0558 

Oil 

56 

4 

758 

958 

.2666 

751 

56 

5 

.14061 

.14202 

7.0410 

.99006 

55 

5 

.15787 

.15988 

6.2549 

.98746 

55 

6 

090 

232 

.0264 

.99002 

54 

6 

816 

.16017 

.2432 

741 

54 

7 

119 

262 

7.0117 

.98998 

53 

7 

845 

047 

.2316 

737 

53 

8 

148 

291 

6.9972 

994 

52 

8 

873 

077 

.2200 

732 

52 

9 

177 

321 

.9827 

990 

51 

9 

902 

107 

.2085 

728 

51 

10 

.14205 

.14351 

6.9682 

.98986 

50 

10 

.15931 

.16137 

6.1970 

.98723 

50 

11 

234 

381 

.9538 

982 

49 

11 

959 

167 

.1856 

718 

49 

12 

263 

410 

.9395 

978 

48 

12 

.15988 

196 

.1742 

714 

48 

13 

292 

440 

.9252 

973 

47 

13 

.16017 

22C 

.1628 

709 

47 

14 

320 

470 

.9110 

969 

46 

14 

046 

256 

.1515 

704 

46 

15 

.14349 

.14499 

6.8969 

.98965 

45 

15 

.16074 

.16286 

6.1402 

.98700 

45 

16 

378 

529 

.8828 

961 

44 

16 

103 

316 

.1290 

695 

44 

17 

407 

559 

.8687 

957 

43 

17 

132 

346 

.1178 

690 

43 

18 

436 

588 

.8548 

953 

42 

18 

160 

376 

.1066 

686 

42 

19 

464 

618 

.8408 

948 

41 

19 

189 

405 

.0955 

681 

41 

20 

.14493 

.14648 

6.8269 

.98944 

40 

20 

.16218 

.16435 

6.0844 

.98676 

40 

21 

522 

678 

.8131 

940 

39 

21 

246 

465 

.0734 

671 

39 

22 

551 

707 

.7994 

936 

38 

22 

275 

495 

.0624 

667 

38 

23 

580 

737 

.7856 

931 

37 

23 

304 

525 

.0514 

662 

37 

24 

608 

767 

.7720 

927 

36 

24 

333 

555 

.0405 

657 

36 

25 

.14637 

.14796 

6.7584 

.98923 

35 

25 

.16361 

.16585 

6.0296 

.98652 

35 

26 

666 

826 

.7448 

919 

34 

26 

390 

615 

.0188 

648 

34 

27 

695 

856 

.7313 

914 

33 

27 

419 

645 

6.0080 

643 

33 

28 

723 

886 

.7179 

910 

32 

28 

447 

674 

5.9972 

638 

32 

29 

752 

915 

.7045 

906 

31 

29 

476 

704 

.9865 

633 

31 

30 

.14781 

.14945 

6.6912 

.98902 

30 

30 

.16505 

.16734 

5.9758 

.98629 

30 

31 

810 

.14975 

.6779 

897 

29 

31 

533 

764 

.9651 

624 

29 

32 

838 

.15005 

.6646 

893 

28 

32 

562 

794 

.9545 

619 

28 

33 

867 

034 

.6514 

889 

27 

33 

591 

824 

.9439 

614 

27 

34 

896 

064 

.6383 

884 

26 

34 

620 

854 

.9333 

609 

26 

35 

.14925 

.15094 

6.6252 

.98880 

25 

35 

.16648 

.16884 

5.9228 

.98604 

25 

36 

954 

124 

.6122 

876 

24 

36 

677 

914 

.9124 

600 

24 

37 

.14982 

153 

.5992 

871 

23 

37 

706 

944 

.9019 

595 

23 

38 

.15011 

183 

.5863 

867 

22 

38 

734 

.16974 

.8915 

590 

22 

39 

040 

213 

.5734 

863 

21 

39 

763 

.17004 

.8811 

585 

21 

40 

.15069 

.15243 

6.5606 

.98858 

20 

40 

.16792 

.17033 

5.8708 

.98580 

20 

41 

097 

272 

.5478 

854 

19 

41 

820 

063 

.8605 

575 

19 

42 

126 

302 

.5350 

849 

18 

42 

849 

093 

.8502 

570 

18 

43 

155 

332 

.5223 

845 

17 

43 

878 

123 

.8400 

565 

17 

44 

184 

362 

.5097 

841 

16 

44 

906 

153 

.8298 

561 

16 

45 

.15212 

.15391 

6.4971 

.98836 

15 

45 

.16935 

.17183 

5.8197 

.98556 

15 

46 

241 

421 

.4846 

832 

14 

46 

964 

213 

.8095 

551 

14 

47 

270 

451 

.4721 

827 

13 

47 

.16992 

243 

.7994 

546 

13 

48 

299 

481 

.4596 

823 

12 

48 

.17021 

273 

.7894 

541 

12 

49 

327 

511 

.4472 

818 

11 

49 

050 

303 

.7794 

536 

11 

50 

.15356 

.15540 

6.4348 

.98814 

10 

50 

.17078 

.17333 

5.7694 

.98531 

10 

51 

385 

570 

.4225 

809 

9 

51 

107 

363 

.7594 

526 

9 

52 

414 

600 

.4103 

805 

8 

52 

136 

393 

.7495 

521 

8 

53 

442 

630 

.3980 

800 

7 

53 

164 

423 

.7396 

516 

7 

54 

471 

660 

.3859 

796 

6 

54 

193 

453 

.7297 

511 

6 

55 

.15500 

.15689 

6.3737 

.98791 

5 

55 

.17222 

.17483 

5.7199 

.98506 

5 

56 

529 

719 

.3617 

787 

4 

56 

250 

513 

.7101 

501 

4 

57 

557 

749 

.3496 

782 

3 

57 

279 

543 

.7004 

496 

3 

58 

586 

779 

.3376 

778 

2 

58 

308 

573 

.6906 

491 

2 

59 

615 

809 

.3257 

773 

1 

59 

336 

603 

.6809 

486 

1 

60 

.15643 

.15838 

6.3138 

.98769 

0 

60 

.17365 

.17633 

5.6713 

.98481 

0 

Cos 

Ctn 

Tan 

Sin 

/ 

Cos 

Ctn 

Tan 

Sin 

/ 

81C 


80C 


II] 


10°  —  Values  of  Trigonometric  Functions  —  11' 


27 


1 

Sin 

Tan 

Ctn 

Cos 

/ 

Sin 

Tan 

Ctn 

Cos 

0 

.17365 

.17633 

5.6713 

.98481 

60 

0 

.19081 

.19438 

5.1446 

.98163 

60 

1 

393 

663 

.6617 

476 

59 

1 

109 

468 

.1366 

157 

59 

2 

422 

693 

.6521 

471 

58 

2 

138 

498 

.1286 

152 

58 

3 

451 

723 

.6425 

466 

57 

3 

167 

529 

.1207 

146 

57 

4 

479 

753 

.6329 

461 

56 

4 

195 

559 

.1128 

140 

56 

5 

.17508 

.17783 

5.6234 

.98455 

55 

5 

.19224 

.19589 

5.1049 

.98135 

55 

6 

537 

813 

.6140 

450 

54 

6 

252 

619 

.0970 

129 

54 

7 

565 

843 

.6045 

445 

53 

7 

281 

649 

.0892 

124 

53 

8 

594 

873 

.5951 

440 

52 

8 

309 

680 

.0814 

118 

52 

9 

623 

903 

.5857 

435 

51 

9 

338 

710 

.0736 

112 

51 

10 

.17651 

.17933 

5.5764 

.98430 

50 

10 

.19366 

.19740 

5.0658 

.98107 

50 

11 

680 

963 

.5671 

425 

49 

11 

395 

770 

.0581 

101 

49 

12 

708 

.17993 

.5578 

420 

48 

12 

423 

801 

.0504 

096 

48 

13 

737 

.18023 

.5485 

414 

47 

13 

452 

831 

.0427 

090 

47 

14 

766 

053 

.5393 

409 

46 

14 

481 

861 

.0350 

084 

46 

15 

.17794 

.18083 

5.5301 

.98404 

45 

15 

.19509 

.19891 

5.0273 

.98079 

45 

16 

823 

113 

.5209 

399 

44 

16 

538 

921 

.0197 

073 

44 

17 

852 

143 

.5118 

394 

43 

17 

566 

952 

.0121 

067 

43 

18 

880 

173 

.5026 

389 

42 

18 

595 

.19982 

5.0045 

061 

42 

19 

909 

203 

.4936 

383 

41 

19 

623 

.20012 

4.9969 

056 

41 

20 

.17937 

.18233 

5.4845 

.98378 

40 

20 

.19652 

.20042 

4.9894 

.98050 

40 

21 

966 

263 

.4755 

373 

39 

21 

680 

073 

.9819 

044 

39 

22 

.17995 

293 

.4665 

368 

38 

22 

709 

103 

.9744 

039 

38 

23 

.18023 

323 

.4575 

362 

37 

23 

737 

133 

.9669 

033 

37 

24 

052 

353 

.4486 

357 

36 

24 

766 

164 

.9594 

027 

36 

25 

.18081 

.18384 

5.4397 

.98352 

35 

25 

.19794 

.20194 

4.9520 

.98021 

35 

26 

109 

414 

.4308 

347 

34 

26 

823 

224 

.9446 

016 

34 

27 

138 

444 

.4219 

341 

33 

27 

851 

254 

.9372 

010 

33 

28 

166 

474 

.4131 

336 

32 

28 

880 

285 

.9298 

.98004 

32 

29 

195 

504 

.4043 

331 

31 

29 

908 

315 

.9225 

.97998 

31 

30 

.18224 

.18534 

5.3955 

.98325 

30 

30 

.19937 

.20345 

4.9152 

.97992 

30 

31 

252 

564 

.3868 

320 

29 

31 

965 

376 

.9078 

987 

29 

32 

281 

594 

.3781 

315 

28 

32 

.19994 

406 

.9006 

981 

28 

33 

309 

624 

.3694 

310 

27 

33 

.20022 

436 

.8933 

975 

27 

34 

338 

654 

.3607 

304 

26 

34 

051 

466 

.8860 

969 

26 

35 

.18367 

.18684 

5.3521 

.98299 

25 

35 

.20079 

.20497 

4.8788 

.97963 

25 

36 

395 

714 

.3435 

294 

24 

36 

108 

527 

.8716 

958 

24 

37 

424 

745 

.3349 

288 

23 

37 

136 

557 

.8644 

952 

23 

38 

452 

775 

.3263 

283 

22 

38 

165 

588 

.8573 

946 

22 

39 

481 

805 

.3178 

277 

21 

39 

193 

618 

.8501 

940 

21 

40 

.18509 

.18835 

5.3093 

.98272 

20 

40 

.20222 

.20648 

4.8430 

.97934 

20 

41 

538 

865 

.3008 

267 

19 

41 

250 

679 

.8359 

928 

19 

42 

567 

895 

.2924 

261 

18 

42 

279 

709 

.8288 

922 

18 

43 

595 

925 

.2839 

256 

17 

43 

307 

739 

.8218 

916 

17 

44 

624 

955 

.2755 

250 

16 

44 

336 

770 

.8147 

910 

16 

45 

.18652 

.18986 

5.2672 

.98245 

15 

45 

.20364 

.20800 

4.8077 

.97905 

15 

46 

681 

.19016 

.2588 

240 

14 

46 

393 

830 

.8007 

899 

14 

47 

710 

046 

.2505 

234 

13 

47 

421 

861 

.7937 

893 

13 

48 

738 

076 

.2422 

229 

12 

48 

450 

891 

.7867 

887 

12 

49 

767 

106 

.2339 

223 

11 

49 

478 

921 

.7798 

881 

11 

50 

.18795 

.19136 

5.2257 

.98218 

10 

50 

.20507 

.20952 

4.7729 

.97875 

10 

51 

824 

166 

.2174 

212 

9 

51 

535 

.20982 

.7659 

869 

9 

52 

852 

197 

.2092 

207 

8 

52 

563 

.21013 

.7591 

863 

8 

53 

881 

227 

.2011 

201 

7 

53 

592 

043 

.7522 

857 

7 

54 

910 

257 

.1929 

196 

6 

54 

620 

073 

.7453 

851 

6 

55 

.18938 

.19287 

5.1848 

.98190 

5 

55 

.20649 

.21104 

4.7385 

.97845 

5 

56 

967 

317 

.1767 

185 

4 

56 

677 

134 

.7317 

839 

4 

57 

.18995 

347 

.1686 

179 

3 

57 

706 

164 

.7249 

833 

3 

58 

.19024 

378 

.1606 

174 

2 

58 

734 

195 

.7181 

827 

2 

•59 

052 

408 

.1526 

168 

1 

59 

763 

225 

.7114 

821 

1 

60 

.19081 

.19438 

5.1446 

.98163 

0 

60 

.20791 

.21256 

4.7046 

.97815 

c 

Cos 

Ctn 

Tan 

Sin 

/ 

Cos 

Ctn 

Tan 

Sin 

/ 

79C 


78C 


28 


12°  —  Values  of  Trigonometric  Functions  —  13C 


[II 


1 

Sin 

Tan 

Ctn 

Cos 

/ 

Sin 

Tan 

Ctn 

Cos 

0 

.20791 

.21256 

4.7046 

.97815 

60 

0 

.22495 

.23087 

4.3315 

.97437 

60 

1 

820 

286 

.6979 

809 

59 

1 

523 

117 

.3257 

430 

59 

2 

848 

316 

.6912 

803 

58 

2 

552 

148 

.3200 

424 

58 

3 

877" 

\  347 

.6845 

797 

57 

3 

580 

179 

.3143 

417 

57 

4 

905- 

1  377 

.6779 

791 

56 

4 

608 

209 

.3086 

411 

56 

5 

.20933 

.21408 

4.6712 

.97784 

55 

5 

.22637 

.23240 

4.3029 

.97404 

55 

6 

962 

438 

.6646 

778 

54 

6 

665 

271 

.2972 

398 

54 

7 

.20990 

469 

.6580 

772 

53 

7 

693 

301 

.2916 

391 

53 

8 

.21019 

499 

.6514 

766 

52 

8 

722 

332 

.2859 

384 

52 

9 

047 

529 

.6448 

760 

51 

9 

750 

363 

.2803 

378 

51 

10 

.21076 

.21560 

4.6382 

.97754 

50 

10 

.22778 

.23393 

4.2747 

.97371 

50 

11 

104 

590 

.6317 

748 

49 

11 

807 

424 

.2691 

365 

49 

12 

132 

621 

.6252 

742 

48 

12 

835 

455 

.2635 

358 

48 

13 

161 

651 

.6187 

735 

47 

13 

863 

485 

.2580 

351 

47 

14 

189 

682 

.6122 

729 

46 

14 

892 

516 

.2524 

345 

46 

15 

.21218 

.21712 

4.6057 

.97723 

45 

15 

.22920 

.23547 

4.2468 

.97338 

45 

16 

246 

743 

.5993 

717 

44 

16 

948 

578 

.2413 

331 

44 

17 

275 

773 

.5928 

711 

43 

17 

.22977 

608 

.2358 

325 

43 

18 

303 

804 

.5864 

705 

42 

18 

.23005 

639 

.2303 

318 

42 

19 

331 

834 

.5800 

698 

41 

19 

033 

670 

.2248 

311 

41 

20 

.21360 

.21864 

4.5736 

.97692 

40 

20 

.23062 

.23700 

4.2193 

.97304 

40 

21 

388 

895 

.5673 

686 

39 

21 

090 

731 

.2139 

298 

39 

22 

417 

925 

.5609 

680 

38 

22 

118 

762 

.2084 

291 

38 

23 

445 

956 

.5546 

673 

37 

23 

146 

793 

.2030 

284 

37 

24 

474 

.21986 

.5483 

667 

36 

24 

175 

823 

.1976 

278 

36 

25 

.21502 

.22017 

4.5420 

.97661 

35 

25 

.23203 

.23854 

4.1922 

.97271 

35 

26 

530 

047 

.5357 

655 

34 

26 

231 

885 

.1868 

264 

34 

27 

559 

078 

.5294 

648 

33 

27 

260 

916 

.1814 

257 

33 

28 

587 

108 

.5232 

642 

32 

28 

288 

946 

.1760 

251 

32 

29 

616 

139 

.5169 

636 

31 

29 

316 

.23977 

.1706 

244 

31 

30 

.21644 

.22169 

4.5107 

.97630 

30 

30 

.23345 

.24008 

4.1653 

.97237 

30 

31 

672 

200 

.5045 

623 

29 

31 

373 

039 

.1600 

230 

29 

32 

701 

231 

.4983 

617 

28 

32 

401 

069 

.1547 

223 

28 

33 

729 

261 

.4922 

611 

27 

33 

429 

100 

.1493 

217 

27 

34 

758 

292 

.4860 

604 

26 

34 

458 

131 

.1441 

210 

26 

35 

36 

.21786 
814 

.22322 
353 

4.4799 
.4737 

.97598 
592 

25 

24 

35 

36 

723"48'6J 
514 

-^4162 
193 

4.1388 
.1335 

.97203 
196 

25 
24 

37 

843 

383 

.4676 

585 

23 

37 

542 

223 

.1282 

189 

23 

38 

871 

414 

.4615 

579 

22 

38 

571 

254 

.1230 

182 

22 

39 

899 

444 

.4555 

573 

21 

39 

599 

285 

.1178 

176 

21 

40 

.21928 

.22475 

4.4494 

.97566 

20 

40 

.23627 

.24316 

4.1126 

.97169 

20 

41 

956 

505 

.4434 

560 

19 

41 

656 

347 

.1074 

162 

19 

42 

.21985 

536 

.4373 

553 

18 

42 

684 

377 

.1022 

155 

18 

43 

.22013 

567 

.4313 

547 

17 

43 

712 

408 

.0970 

148 

17 

44 

041 

597 

.4253 

541 

16 

44 

740 

439 

.0918 

141 

16 

45 

.22070 

.22628 

4.4194 

.97534 

15 

45 

.23769 

.24470 

4.0867 

.9*134 

15 

46 

098 

658 

.4134 

528 

14 

46 

797 

501 

.0815 

127 

14 

47 

126 

689 

.4075 

521 

13 

47 

825 

532 

.0764 

120 

13 

48 

155 

719 

.4015 

515 

12 

48 

853 

562 

.0713 

113 

12 

49 

183 

750 

.3956 

508 

11 

49 

882 

593 

.0662 

106 

11 

50 

.22212 

.22781 

4.3897 

.97502 

10 

50 

.23910 

.24624 

4.0611 

.97100 

10 

51 

240 

811 

.3838 

496 

9 

51 

938 

655 

.0560 

093 

9 

52 

268 

842 

.3779 

489 

8 

52 

966 

686 

.0509 

086 

8 

53 

297 

872 

.3721 

483 

7 

53 

.23995 

717 

.0459 

079 

7 

54 

325 

903 

.3662 

476 

6 

54 

.24023 

747 

.0408 

072 

6 

55 

.22353 

.22934 

4.3604 

.97470 

5 

55 

.24051 

.24778 

4.0358 

.97065 

5 

56 

382 

964 

.3546 

463 

4 

56 

079 

809 

.0308 

058 

4 

57 

410 

.22995 

.3488 

457 

3 

57 

108 

840 

.0257 

051 

3 

58 

438 

.23026 

.3430 

450 

2 

58 

136 

871 

.0207 

044 

2 

59 

467 

056 

.3372 

444 

1 

59 

164 

902 

.0158 

037 

1 

60 

.22495 

.23087 

4.3315 

.97437 

0 

60 

.24192 

.24933 

4.0108 

.97030 

0 

Cos 

Ctn 

Tan 

Sin 

' 

Cos 

Ctn 

Tan 

Sin 

/ 

IT 


76C 


II]          14°  —  Values  of  Trigonometric  Functions  —  15C 


29 


1 

Sin 

Tan 

Ctn 

Cos 

/ 

Sin 

Tan 

Ctn 

Cos 

0 

.24192 

.24933 

4.0108 

.97030 

60 

0 

.25882 

.26795 

3.7321 

.96593 

60 

1 

220 

964 

.0058 

023 

59 

1 

910 

826 

.7277 

585 

59 

2 

249 

.24995 

4.0009 

015 

58 

2 

938 

857 

.7234 

578 

58 

3 

277 

.25026 

3.9959 

008 

57 

3 

966 

888 

.7191 

570 

57 

4 

305 

056 

.9910 

.97001 

56 

4 

.25994 

920 

.7148 

562 

56 

5 

.24333 

.25087 

3.9861 

.96994 

55 

5 

.26022 

.26951 

3.7105 

.96555 

55 

6 

362 

118 

.9812 

987 

54 

6 

050 

.26982 

.7062 

547 

54 

7 

390 

149 

.9763 

980 

53 

7 

079 

.27013 

.7019 

540 

53 

8 

418 

180 

.9714 

973 

52 

8 

107 

044 

.6976 

532 

52 

9 

446 

211 

.9665 

966 

51 

9 

135 

076 

.6933 

524 

51 

10 

.24474 

.25242 

3.9617 

.96959 

50 

10 

.26163 

.27107 

3.6891 

.96517 

50 

11 

503 

273 

.9568 

952 

49 

11 

191 

138 

.6848 

509 

49 

12 

531 

304 

.9520 

945 

48 

12 

219 

169 

.6806 

502 

48 

13 

559 

335 

.9471 

937 

47 

13 

247 

201 

.6764 

494 

47 

14 

587 

366 

.9423 

930 

46 

14 

275 

232 

.6722 

486 

46 

15 

.24615 

.25397 

3.9375 

.96923 

45 

15 

.26303 

.27263 

3.6680 

.96479 

45 

16 

644 

428 

.9327 

916 

44 

16 

__334- 

-  —  294 

.6638 

471 

44 

17 

672 

459 

.9279 

909 

43 

17 

359 

326 

.6596 

463 

43 

18 

700 

490 

.9232 

902 

42 

18 

387 

357 

.6554 

456 

42 

19 

728 

521 

.9184 

894 

41 

19 

415 

388 

.6512 

448 

41 

20 

.24756 

.25552 

3.9136 

.96887 

40 

20 

.26443 

.27419 

3.6470 

.96440 

40 

21 

784 

583 

.9089 

880 

39 

21 

471 

451 

.6429 

433 

39 

22 

813 

614 

.9042 

873 

38 

22 

500 

482 

.6387 

425 

38 

23 

841 

645 

.8995 

866 

37 

23 

528 

513 

.6346 

417 

37 

24 

869 

676 

.8947 

858 

36 

24 

556 

545 

.6305 

410 

36 

25 

.24897 

.25707 

3.8900 

.96851 

35 

25 

.26584 

.27576 

3.6264 

.96402 

35 

26 

925 

738 

.8854 

844 

34 

26 

612 

607 

.6222 

394 

34 

27 

954 

769 

.8807 

837 

33 

27 

640 

638 

.6181 

386 

33 

28 

:2?9S2 

"  800 

.8760 

829 

32 

28 

668 

670 

.6140 

379 

32 

29 

.25010 

831 

.8714 

822 

31 

29 

696 

701 

.6100 

371 

31 

30 

.25038 

.25862 

3.8667 

.96815 

30 

30 

.26724 

.27732 

3.6059 

.96363 

30 

31 

066 

893 

.8621 

807 

29 

31 

752 

764 

.6018 

355 

29 

32 

094 

924 

.8575 

800 

28 

32 

780 

795 

.5978 

347 

28 

33 

122 

955 

.8528 

793 

27 

33 

808 

826 

.5937 

340 

27 

34 

151 

.25986 

.8482 

786 

26 

34 

836 

858 

.5897 

332 

26 

35 

.25179 

.26017 

3.8436 

.96778 

25 

35 

.26864 

.27889 

3.5856 

.96324 

25 

36 

207 

048 

.8391 

771 

24 

36 

892 

921 

.5816 

316 

24 

37 

235 

079 

.8345 

764 

23 

37 

920 

952 

.5776 

308 

23 

38 

263 

110 

.8299 

756 

22 

38 

948 

.27983 

.5736 

301 

22 

39 

291 

141 

.8254 

749 

21 

39 

.26976 

.28015 

.5696 

293 

21 

40 

.25320 

.26172 

3.8208 

.96742 

20 

40 

.27004 

.28046 

3.5656 

.96285 

20 

41 

348 

203 

.8163 

734 

19 

41 

032 

077 

.5616 

277 

19 

42 

376 

235 

.8118 

727 

18 

42 

060 

109 

.5576 

269 

18 

43 

404 

266 

.8073 

719 

17 

43 

088 

140 

.5536 

261 

17 

44 

432 

297 

.8028 

712 

16 

44 

116 

172 

.5497 

253 

16 

45 

.25460 

.26328 

3.7983 

.96705 

15 

45 

.27144 

.28203 

3.5457 

.96246 

15 

46 

488 

359 

.7938 

697 

14 

46 

172 

234 

.5418 

238 

14 

47 

516 

390 

.7893 

690 

13 

47 

200 

266 

.5379 

230 

13 

48 

545 

421 

.7848 

682 

12 

48 

228 

297 

.5339 

222 

12 

49 

573 

452 

.7804 

675 

11 

49 

256 

329 

.5300 

214 

11 

50 

.25601 

.26483 

3.7760 

.96667 

10 

50 

.27284 

.28360 

3.5261 

.96206 

10 

51 

629 

515 

.7715 

660 

9 

51 

312 

391 

.5222 

198 

9 

52 

657 

546 

.7671 

653 

8 

52 

340 

423 

.5183 

190 

8 

53 

685 

577 

.7627 

645 

7 

53 

368 

454 

.5144 

182 

7 

54 

713 

608 

.7583 

638 

6 

54 

396 

486 

.5105 

174 

6 

55 

.25741 

.26639 

3.7539 

.96630 

5 

55 

.27424 

.28517 

3.5067 

.96166 

5 

56 

769 

670 

.7495 

623 

4 

56 

452 

549 

.5028 

158 

4 

57 

798 

701 

.7451 

615 

3 

57 

480 

580 

.4989 

150 

3 

58 

826 

733 

.7408 

608 

2 

58 

508 

612 

.4951 

142 

2 

59 

854 

764 

.7364 

600 

1 

59 

536 

643 

.4912 

134 

1 

60 

.25882 

.26795 

3.7321 

.96593 

0 

60 

.27504 

.28675 

3.4874 

.96126 

_0_ 

Cos 

Ctn 

Tan 

Sin 

/ 

COG 

Ctn 

Tan 

Sin 

/ 

75C 


74C 


30 


16°  —  Values  of  Trigonometric  Functions  —  17C 


[11 


1 

Sin 

Tan 

Ctn 

Cos 

' 

Sin 

Tan 

Ctn 

Cos 

0 

.27564 

.28675 

3.4874 

.96126 

60 

0 

.29237 

.30573 

3.2709 

.95630 

60 

1 

592 

706 

.4836 

118 

59 

1 

265 

605 

.2675 

622 

59 

2 

620 

738 

.4798 

110 

58 

2 

293 

637 

.2641 

613 

58 

3 

648 

769 

.4760 

102 

57 

3 

321 

669 

.2607 

605 

57 

4 

676/ 

801 

.4722 

094 

56 

4 

348 

700 

.2573 

596 

56 

5 

.27704- 

.28832 

3.4684 

.96086 

55 

5 

.29376 

.30732 

3.2539 

.95588 

55 

6 

731 

,  ,864 

.4646 

078 

54 

6 

404 

764 

.2506 

579 

54 

7 

759 

'  895 

.4608 

070 

53 

7 

432 

796 

.2472 

571 

53 

8 

787 

927 

.4570 

062 

52 

8 

460 

828 

.2438 

562 

52 

9 

815 

958 

.4533 

054 

51 

9 

487 

860 

.2405 

554 

51 

10 

.27843 

.28990 

3.4495 

.96046 

50 

10 

.29515 

.30891 

3.2371 

.95545 

50 

11 

871 

.29021 

.4458 

037 

49 

11 

543 

923 

.2338 

536 

49 

12 

899 

053 

.4420 

029 

48 

12 

571 

955 

.2305 

528 

48 

13 

927 

084 

.4383 

021 

47 

13 

599 

.30987 

.2272 

519 

47 

14 

955 

116 

.4346 

013 

46 

14 

626 

.31019 

.2238 

511 

46 

15 

.27983 

.29147 

3.4308 

.96005 

45 

15 

.29654 

.31051 

3.2205 

.95502 

45 

16 

.28011 

179 

.4271 

.95997 

44 

16 

682 

083 

.2172 

493 

44 

17 

039 

210 

.4234 

989 

43 

17 

710 

115 

.2139 

485 

43 

18 

067 

242 

.4197 

981 

42 

18 

737 

147 

.2106 

476 

42 

19 

095 

274 

.4160 

972 

41 

19 

765 

178 

.2073 

467 

41 

20 

.28123 

.29305 

3.4124 

.95964 

40 

20 

.29793 

.31210 

3.2041 

.95459 

40 

21 

150 

337 

.4087 

956 

39 

21 

821 

242 

.2008 

450 

39 

22 

178 

368 

.4050 

948 

38 

22 

849 

274 

.1975 

441 

38 

23 

206 

400 

.4014 

940 

37 

23 

876 

306 

.1943 

433 

37 

24 

234 

432 

.3977 

931 

36 

24 

904 

338 

.1910 

424 

36 

25 

.28262 

.29463 

3.3941 

.95923 

35 

25 

.29932 

.31370 

3.1878 

.95415 

35 

26 

290 

495 

.3904 

915 

34 

26 

960 

402 

.1845 

407 

34 

27 

318 

526 

.3868 

907 

33 

27 

.29987 

434 

.1813 

398 

33 

28 

346 

558 

.3832 

898 

32 

28 

.30015 

466 

.1780 

389 

32 

29 

374 

590 

.3796 

890 

31 

29 

043 

498 

.1748 

380 

31 

30 

.28402 

.29621 

3.3759 

.95882 

30 

30 

.30071 

.31530 

3.1716 

.95372 

30 

31 

429 

653 

.3723 

874 

29 

31 

098 

562 

.1684 

363 

29 

32 

457 

685 

.3687 

865 

28 

32 

126 

594 

.1652 

354 

28 

33 

485 

716 

.3652 

857 

27 

33 

154 

626 

.1620 

345 

27 

34 

513 

748 

.3616 

849 

26 

34 

182 

658 

.1588 

337 

26 

35 

.28541 

.29780 

3.3580 

.95841 

25 

35 

.30209 

.31690 

3.1556 

.95328 

25 

36 

569 

811 

.3544 

832 

24 

36 

237 

722 

.1524 

319 

24 

37 

597 

843 

.3509 

824 

23 

37 

265 

754 

.1492 

310 

23 

38 

625 

875 

.3473 

816 

22 

38 

292 

786 

.1460 

301 

22 

39 

652 

906 

.3438 

807 

21 

39 

320 

818 

.1429 

293 

21 

40 

.28680 

.29938 

3.3402 

.95799 

20 

40 

.30348 

.31850 

3.1397 

.95284 

20 

41 

708 

.29970 

.3367 

791 

19 

41 

376 

882 

.1366 

275 

19 

42 

736 

.30001 

.3332 

782 

18 

42 

403 

914 

.1334 

266 

18 

43 

764 

033 

.3297 

774 

17 

43 

431 

946 

.1303 

257 

17 

44 

792 

065 

.3261 

766 

16 

44 

459 

.31978 

.1271 

248 

16 

45 

.28820 

.30097 

3.3226 

.95757 

15 

45 

.30486 

.32010 

3.1240 

.95240 

15 

46 

847 

128 

.3191 

749 

14 

46 

514 

042 

.1209 

231 

14 

47 

875 

160 

.3156 

740 

13 

47 

542 

074 

.1178 

222 

13 

48 

903 

192 

.3122 

732 

12 

48 

570 

106 

.1146 

213 

12 

49 

931 

224 

.3087 

724 

11 

49 

597 

139 

.1115 

204 

11 

50 

.28959 

.30255 

3.3052 

.95715 

10 

50 

.30625 

.32171 

3.1084 

.95195 

10 

51 

.28987 

287 

.3017 

707 

9 

51 

653 

203 

.1053 

186 

9 

52 

.29015 

319 

.2983 

698 

8 

52 

680 

235 

.1022 

177 

8 

53 

042 

351 

.2948 

690 

7 

53 

708 

267 

.0991 

168 

7 

54 

070 

382 

.2914 

681 

6 

54 

736 

299 

.0961 

159 

6 

55 

.29098 

.30414 

3.2879 

.95673 

5 

55 

.30763 

.32331 

3.0930 

.95150 

5 

56 

126 

446 

.2845 

664 

4 

56 

791 

363 

.0899 

142 

4 

57 

154 

478 

.2811 

656 

3 

57 

819 

396 

.0868 

133 

3 

58 

182 

509 

.2777 

647 

2 

58 

846 

428 

.0838 

124 

2 

59 

209 

541 

.2743 

639 

1 

59 

874 

460 

.0807 

115 

1 

60 

.29237 

.30573 

3.2709 

.95630 

0 

60 

.30902 

.32492 

3.0777 

.95106 

0 

Cos 

Ctn 

Tan 

Sin 

/ 

Cos 

Ctn 

Tan 

Sin  J 

' 

73C 


72C 


II] 


18°  —  Values  of  Trigonometric  Functions  —  19° 


31 


1 

Sin 

Tan 

Ctn 

Cos 

/ 

Sin 

Tan 

Ctn 

Cos 

0 

.30902 

.32492 

3.0777 

.95106 

60 

0 

.32557 

.34433 

2.9042 

.94552 

60 

1 

929 

524 

.0746 

097 

59 

1 

584 

465 

.9015 

542 

59 

2 

957 

556 

.0716 

088 

58 

2 

612 

498 

.8987 

533 

58 

3 

.30985 

588 

.0686 

079 

57 

3 

639 

530 

.8960 

523 

57 

4 

.31012 

621 

.0655 

070 

56 

4 

667 

563 

.8933 

514 

56 

5 

.31040 

.32653 

3.0625 

.95061 

55 

5 

.32694 

.34596 

2.8905 

.94504 

55 

6 

068 

685 

.0595 

052 

54 

6 

722 

628 

.8878 

495 

54 

7 

095 

717 

.0565 

043 

53 

7 

749 

661 

.8851 

485 

53 

8 

123 

749 

.0535 

033 

52 

8 

777 

693 

.8824 

476 

52 

9 

151 

782 

.0505 

024 

51 

9 

804 

726 

.8797 

466 

51 

10 

.31178 

.32814 

3.0475 

.95015 

50 

10 

.32832 

.34758 

2.8770 

.94457 

50 

11 

206 

846 

.0445 

.95006 

49 

11 

859 

791 

.8743 

447 

49 

12 

233 

878 

.0415 

.94997 

48 

12 

88^ 

824 

.8716 

438 

48 

13 

261 

911 

.0385 

988 

47 

13 

914 

856 

.8689 

428 

47 

14 

289 

943 

.0356 

979 

46 

14 

942 

889 

.8662 

418 

46 

15 

.31316 

.32975 

3.0326 

.94970 

45 

15 

.32969 

.34922 

2.8636 

.94409 

45 

16 

344 

.33007 

.0296 

961 

44 

16 

.32997 

954 

.8609 

399 

44 

17 

372 

040 

.0267 

952 

43 

17 

.33024 

.34987 

.8582 

390 

43 

18 

399 

072 

.0237 

943 

42 

18 

051 

.35020 

.8556 

380 

42 

19 

427 

104 

.0208 

933 

41 

19 

079 

052 

.8529 

370 

41 

20 

.31454 

.33136 

3.0178 

.94924 

40 

20 

.33106 

.35085 

2.8502 

.94361 

40 

21 

482 

169 

.0149 

915 

39 

21 

134 

118 

.8476 

351 

39 

22 

510 

201 

.0120 

906 

38 

22 

161 

150 

.8449 

342 

38 

23 

537 

233 

.0090 

897 

37 

23 

189 

183 

.8423 

332 

37 

24 

565 

266 

.0061 

888 

36 

24 

216 

216 

.8397 

322 

36 

25 

.31593 

.33298 

3.0032 

.94878 

35 

25 

.33244 

.35248 

2.8370 

.94313 

35 

26 

620 

330 

3.0003 

869 

34 

26 

271 

281 

.8344 

303 

34 

27 

648 

363 

2.9974 

860 

33 

27 

298 

314 

.8318 

293 

33 

28 

675 

395 

.9945 

851 

32 

28 

326 

346 

.8291 

284 

32 

29 

703 

427 

.9916 

842 

31 

29 

353 

379 

.8265 

274 

31 

30 

.31730 

.33460 

2.9887 

.94832 

30 

30 

.33381 

.35412 

2.8239 

.94264 

30 

31 

758 

492 

.9858 

823 

29 

31 

408 

445 

.8213 

254 

29 

32 

786 

524 

.9829 

814 

28 

32 

436 

477 

.8187 

245 

28 

33 

813 

557 

.9800 

805 

27 

33 

463 

510 

.8161 

235 

27 

34 

841 

589 

.9772 

795 

26 

34 

490 

543 

.8135 

225 

26 

35 

.31868 

.33621 

2.9743 

.94786 

25 

35 

.33518 

.35576 

2.8109 

.94215 

25 

36 

896 

654 

.9714 

111 

24 

36 

545 

608 

.8083 

206 

24 

37 

923 

686 

.9686 

768 

23 

37 

573 

641 

.8057 

196 

23 

38 

951 

718 

.9657 

758 

22 

38 

600 

674 

.8032 

186 

22 

39 

.31979 

751 

.9629 

749 

21 

39 

627 

707 

.8006 

176 

21 

40 

.32006 

.33783 

2.9600 

.94740 

20 

40 

.33655 

.35740 

2.7980 

.94167 

20 

41 

034 

816 

.9572 

730 

19 

41 

682 

772 

.7955 

157 

19 

42 

061 

848 

.9544 

721 

18 

42 

710 

805 

.7929 

147 

18 

43 

089 

881 

.9515 

712 

17 

43 

737 

838 

.7903 

137 

17 

44 

116 

913 

.9487 

702 

16 

44 

764 

871 

.7878 

127 

16 

45 

.32144 

.33945 

2.9459 

.94693 

15 

45 

.33792 

.35904 

2.7852 

.94118 

15 

46 

171 

.33978 

.9431 

684 

14 

46 

819 

937 

.7827 

108 

14 

47 

199 

.34010 

.9403 

674 

13 

47 

846 

.35969 

.7801 

098 

13 

48 

227 

043 

.9375 

665 

12 

48 

874 

.36002 

.7776 

088 

12 

49 

254 

075 

.9347 

656 

11 

49 

901 

035 

.7751 

078 

11 

50 

.32282 

.34108 

2.9319 

.94646 

10 

50 

.33929 

.36068 

2.7725 

.94068 

10 

51 

309 

140 

.9291 

637 

9 

51 

956 

101 

.7700 

058 

9 

52 

337 

173 

.9263 

627 

8 

52 

.33983 

134 

.7675 

049 

8 

53 

364 

205 

.9235 

618 

7 

53 

.34011 

167 

.7650 

039 

7 

54 

392 

238 

.9208 

609 

6 

54 

038 

199 

.7625 

029 

6 

55 

.32419 

.34270 

2.9180 

.94599 

5 

55 

.34065 

.36232 

2.7600 

.94019 

5 

56 

447 

303 

.9152 

590 

4 

56 

093 

265 

.7575 

.94009 

4 

57 

474 

335 

.9125 

580 

3 

57 

120 

298 

.7550 

.93999 

3 

58 

502 

368 

.9097 

571 

2 

58 

147 

331 

.7525 

989 

2 

59 

529 

400 

.9070 

561 

1 

59 

175 

364 

.7500 

979 

1 

60 

.32557 

.34433 

2.9042 

.94552 

0 

60 

.34202 

.36397 

2.7475 

.93969 

0 

Cos 

Ctn 

Tan 

Sin 

' 

Cos 

Ctn 

Tan   Sin 

/ 

71C 


70° 


32 


20°  —  Values  of  Trigonometric  Functions  —  2V 


[II 


/ 

Sin 

Tan 

Ctn 

Cos 

1 

Sin 

Tan 

Ctn 

Cos 

0 

.34202 

.36397 

2.7475 

.93969 

60 

0 

.35837 

.38386 

2.6051 

.93358 

60 

1 

229 

430 

.7450 

959 

59 

1 

864 

420 

.6028 

348 

59 

2 

257 

463 

.7425 

949 

58 

2 

891 

453 

.6006 

337 

58 

3 

284 

496 

.7400 

939 

57 

3 

918 

487 

.5983 

327 

57 

4 

311 

529 

.7376 

929 

56 

4 

945 

520 

.5961 

316 

56 

5 

.34339 

.36562 

2.7351 

.93919 

55 

5 

.35973 

.38553 

2.5938 

.93306 

55 

6 

366 

595 

.7326 

909 

54 

6 

.36000 

587 

.5916 

295 

54 

7 

393 

628 

.7302 

899 

53 

7 

027 

620 

.5893 

285 

53 

8 

421 

661 

.7277 

889 

52 

8 

054 

654 

.5871 

274 

52 

9 

448 

694 

.7253 

879 

51 

9 

081 

687 

.5848 

264 

51 

10 

.34475 

.36727 

2.7228 

.93869 

50 

10 

.36108 

.38721 

2.5826 

.93253 

50 

11 

503 

760 

.7204 

859 

49 

11 

135 

754 

.5804 

243 

49 

12 

530 

793 

.7179 

849 

48 

12 

162 

787 

.5782 

232 

48 

13 

557 

826 

.7155 

839 

47 

13 

190 

821 

.5759 

222 

47 

14 

584 

859 

.7130 

829 

46 

14 

217 

854 

.5737 

211 

46 

15 

.34612 

.36892 

2.7106 

.93819 

45 

15 

.36244 

.38888 

2.5715 

.93201 

45 

16 

639 

925 

.7082 

809 

44 

16 

271 

921 

.5693 

190 

44 

17 

666 

958 

.7058 

799 

43 

17 

298 

955 

.5671 

180 

43 

18 

694 

.36991 

.7034 

789 

42 

18 

325 

.38988 

.5649 

169 

42 

19 

721 

.37024 

.7009 

779 

41 

19 

352 

.39022 

.5627 

159 

41 

20 

.34748 

.37057 

2.6985 

.93769 

40 

20 

.36379 

.39055 

2.5605 

.93148 

40 

21 

775 

090 

.6961 

759 

39 

21 

406 

089 

.5583 

137 

39 

22 

803 

123 

.6937 

748 

38 

22 

434 

122 

.5561 

127 

38 

23 

830 

157 

.6913 

738 

37 

23 

461 

156 

.5539 

116 

37 

24 

857 

190 

.6889 

728 

36 

24 

488 

190 

.5517 

106 

36 

25 

.34884 

.37223 

2.6865 

.93718 

35 

25 

.36515 

.39223 

2.5495 

.93095 

35 

26 

912 

256 

.6841 

708 

34 

26 

542 

257 

.5473 

084 

34 

27 

939 

289 

.6818 

698 

33 

27 

569 

290 

.5452 

074 

33 

28 

966 

322 

.6794 

688 

32 

28 

596 

324 

.5430 

063 

32 

29 

.34993 

355 

.6770 

677 

31 

29 

623 

357 

.5408 

052 

31 

30 

.35021 

.37388 

2.6746 

.93667 

30 

30 

.36650 

.39391 

2.5386 

.93042 

30 

31 

048 

422 

.6723 

657 

29 

31 

677 

425 

.5365 

031 

29 

32 

075 

455 

.6699 

647 

28 

32 

704 

458 

.5343 

020 

28 

33 

102 

488 

.6675 

637 

27 

33 

731 

492 

.5322 

.93010 

27 

34 

130 

521 

.6652 

626 

26 

34 

758 

526 

.5300 

.92999 

26 

35 

.35157 

.37554 

2.6628 

.93616 

25 

35 

.36785 

.39559 

2.5279 

.92988 

25 

36 

184 

588 

.6605 

606 

24 

36 

812 

593 

.5257 

978 

24 

37 

211 

621 

.6581 

596 

23 

37 

839 

626 

.5236 

967 

23 

38 

239 

654 

.6558 

585 

22 

38 

867 

660 

.5214 

956 

22 

39 

266 

687 

.6534 

575 

21 

39 

894 

694 

.5193 

945 

21 

40 

.35293 

.37720 

2.6511 

.93565 

20 

40 

.36921 

.39727 

2.5172 

.92935 

20 

41 

320 

754 

.6488 

555 

19 

41 

948 

761 

.5150 

924 

19 

42 

347 

787 

.6464 

544 

18 

42 

.36975 

795 

.5129 

913 

18 

43 

375 

820 

.6441 

534 

17 

43 

.37002 

829 

.5108 

902 

17 

44 

402 

853 

.6418 

524 

16 

44 

029 

862 

.5086 

892 

16 

45 

.35429 

.37887 

2.6395 

.93514 

15 

45 

.37056 

.39896 

2.5065 

.92881 

15 

46 

456 

920 

.6371 

503 

14 

46 

083 

930 

.5044 

870 

14 

47 

484 

953 

.6348 

493 

13 

47 

110 

963 

.5023 

859 

13 

48 

511 

.37986 

.6325 

483 

12 

48 

137 

.39997 

.5002 

849 

12 

49 

538 

.38020 

.6302 

472 

11 

49 

164 

.40031 

.4981 

838 

11 

50 

.35565 

.38053 

2.6279 

.93462 

10 

50 

.37191 

.40065 

2.4960 

.92827 

10 

51 

592 

086 

.6256 

452 

9 

51 

218 

098 

.4939 

816 

9 

52 

619 

120 

.6233 

441 

8 

52 

245 

132 

.4918 

805 

8 

53 

647 

153 

.6210 

431 

7 

53 

272 

166 

.4897 

794 

7 

54 

674 

186 

.6187 

420 

6 

54 

299 

200 

.4876 

784 

6 

55 

.35701 

.38220 

2.6165 

.93410 

5 

55 

.37326 

.40234 

2.4855 

.92773 

5 

56 

728 

253 

.6142 

400 

4 

56 

353 

267 

.4834 

762 

4 

57 

755 

286 

.6119 

389 

3 

57 

380 

301 

.4813 

751 

3 

58 

782 

320 

.6096 

379 

2 

58 

407 

335 

.4792 

740 

2 

59 

810 

353 

.6074 

368 

1 

59 

434 

369 

.4772 

729 

1 

60 

.35837 

.38386 

2.6051 

.93358 

c 

60 

.37461 

.40403 

2.4751 

.92718 

0 

Cos 

Ctn 

Tan 

Sin 

1 

Cos 

Ctn 

Tan 

Sin 

i 

69C 


68C 


II]         22°  —  Values  of  Trigonometric  Functions  —  23C 


33 


/ 

Sin 

Tan 

Ctn 

Cos 

' 

Sin 

Tan 

Ctn 

Cos 

0 

.37461 

.40403 

2.4751 

.92718 

60 

0 

.39073 

.42447 

2.3559 

.92050 

60 

1 

488 

436 

.4730 

707 

59 

1 

100 

482 

.3539 

039 

59 

2 

515 

470 

.4709 

697 

58 

2 

127 

516 

.3520 

028 

58 

3 

542 

504 

.4689 

686 

57 

3 

153 

551 

.3501 

016 

57 

4 

569 

538 

.4668 

675 

56 

4 

180 

585 

.3483 

.92005 

56 

5 

.37595 

.40572 

2.4648 

.92664 

55 

5 

.39207 

.42619 

2.3464 

.91994 

55 

6 

622 

606 

.4627 

653 

54 

6 

234 

654 

.3445 

982 

54 

7 

649 

640 

.4606 

642 

53 

7 

260 

688 

.3426 

971 

53 

8 

676 

674 

.4586 

631 

52 

8 

287 

722 

.3407 

959 

52 

9 

703 

707 

.4566 

620 

51 

9 

314 

757 

.3388 

948 

51 

10 

.37730 

.40741 

2.4545 

.92609 

50 

10 

.39341 

.42791 

2.3369 

.91936 

50 

11 

757 

775 

.4525 

598 

49 

11 

367 

826 

.3351 

925 

49 

12 

784 

809 

.4504 

587 

48 

12 

394 

860 

.3332 

914 

48 

13 

811 

843 

.4484 

576 

47 

13 

421 

894 

.3313 

902 

47 

14 

838 

877 

.4464 

565 

46 

14 

448 

929 

.3294 

891 

46 

15 

.37865 

.40911 

2.4443 

.92554 

45 

15 

.39474 

.42963 

2.3276 

.91879 

45 

16 

892 

945 

.4423 

543 

44 

16 

501 

.42998 

.3257 

868 

44 

17 

919 

.40979 

.4403 

532 

43 

17 

528 

.43032 

.3238 

856 

43 

18 

946 

.41013 

.4383 

521 

42 

18 

555 

067 

.3220 

845 

42 

19 

973 

047 

.4362 

510 

41 

19 

581 

101 

.3201 

833 

41 

20 

.37999 

.41081 

2.4342 

.92499 

40 

20 

.39608 

.43136 

2.3183 

.91822 

40 

21 

.38026 

115 

.4322 

488 

39 

21 

635 

170 

.3164 

810 

39 

22 

053 

149 

.4302 

477 

38 

22 

661 

205 

.3146 

799 

38 

23 

080 

183 

.4282 

466 

37 

23 

688 

239 

.3127 

787 

37 

24 

107 

217 

.4262 

455 

36 

24 

715 

274 

.3109 

775 

36 

25 

.38134 

.41251 

2.4242 

.92444 

35 

25 

.39741 

.43308 

2.3090 

.91764 

35 

26 

161 

285 

.4222 

432 

34 

26 

768 

343 

.3072 

752 

34 

27 

188 

319 

.4202 

421 

33 

27 

795 

378 

.3053 

741 

33 

28 

215 

353 

.4182 

410 

32 

28 

822 

412 

.3035 

729 

32 

29 

241 

387 

.4162 

399 

31 

29 

848 

447 

.3017 

718 

31 

30 

.38268 

.41421 

2.4142 

.92388 

30 

30 

.39875 

.43481 

2.2998 

.91706 

30 

31 

295 

455 

.4122 

377 

29 

31 

902V 

516 

.2980 

694 

29 

32 

322 

490 

.4102 

366 

28 

32 

928 

•  550 

.2962 

683 

28 

33 

349 

524 

.4083 

355 

27 

33 

955 

-  585 

.2944 

671 

27 

34 

376 

558 

.4063 

343 

26 

34 

~30Q82 

620 

.2925 

660 

26 

35 

.38403 

.41592 

2.4043 

.92332 

25 

35 

.40008 

\43654 

2.2907 

.91648 

25 

36 

430 

626 

.4023 

321 

24 

36 

035 

689 

.2889 

636 

24 

37 

456 

660 

.4004 

310 

23 

37 

062 

724 

.2871" 

625 

23 

38 

483 

694 

.3984 

299 

22 

38 

088 

758 

.2853 

613 

22 

39 

510 

728 

.3964 

287 

21 

39 

115 

793 

.2835 

601 

21 

40 

.38537 

.41763 

2.3945 

.92276 

20 

40 

.40141 

.43828 

2.2817 

.91590 

20 

41 

564 

797 

.3925 

265 

19 

41 

168 

862 

.2799 

578 

19 

42 

591 

831 

.3906 

254 

18 

42 

195 

897 

.2781 

566 

18 

43 

617 

865 

.3886 

243 

17 

43 

221 

932 

.2763 

555 

17 

44 

644 

899 

.3867 

231 

16 

44 

248 

.43966 

.2745 

543 

16 

45 

.38671 

.41933 

2.3847 

.92220 

15 

45 

.40275 

.44001 

2.2727 

.91531 

15 

46 

698 

.41968 

.3828 

209 

14 

46 

301 

036 

.2709 

519- 

14 

47 

725 

.42002 

.3808 

198 

13 

47 

328 

071 

.2691 

508 

13 

48 

752 

036 

.3789 

186 

12 

48 

355 

105 

.2673 

496 

12 

49 

778 

070 

.3770 

175 

11 

49 

381 

140 

.2655 

484 

11 

50 

.38805 

.42105 

2.3750 

.92164 

10 

50 

.40408 

.44175 

2.2637 

.91472 

10 

51 

832 

139 

.3731 

152 

9 

51 

434 

210 

.2620 

461 

9 

52 

859 

173 

.3712 

141 

8 

52 

461 

244 

.2602 

449 

8 

53 

886 

207 

.3693 

130 

7 

53 

488 

279 

.2584 

437 

7 

54 

912 

242 

.3673 

119 

6 

54 

514 

314 

.2566 

425 

6 

55 

.38939 

.42276 

2.3654 

.92107 

5 

55 

.40541 

.44349 

2.2549 

.91414 

5 

56 

966 

310 

.3635 

096 

4 

56 

567 

384 

.2531 

402 

4 

57 

.38993 

345 

.3616 

085 

3 

57 

594 

418 

.2513 

390 

3 

58 

.39020 

379 

.3597 

073 

2 

58 

621 

453 

.2496 

378 

2 

59 

046 

413 

.3578 

062 

1 

59 

647 

488 

.2478 

366 

1 

60 

.39073 

.42447 

2.3559 

.92050 

0 

60 

.40674 

.44523 

2.2460 

.91355 

0 

Cos 

Ctn 

Tan 

Sin 

/ 

Cos 

Ctn 

Tan 

Sin 

i 

67C 


66C 


34 


24°  —  Values  of  Trigonometric  Functions  —  25C 


/ 

Sin 

Tan 

Ctn 

Cos 

/ 

Sin 

Tan 

Ctn 

Cos 

0 

.40674 

.44523 

2.2460 

.91355 

60 

0 

.42262 

.46631 

2.1445 

.90631 

60 

1 

700 

558 

.2443 

343 

59 

1 

288 

666 

.1429 

618 

59 

2 

727 

593 

.2425 

331 

58 

2 

315 

702 

.1413 

606 

58 

3 

753 

627 

.2408 

319 

57 

3 

341 

737 

.1396 

594 

57 

4 

780 

662 

.2390 

307 

56 

4 

367 

772 

.1380 

582 

56 

5 

.40806 

.44697 

2.2373 

.91295 

55 

5 

.42394 

.46808 

2.1364 

.90569 

55 

6 

833 

732 

.2355 

283 

54 

6 

420 

843 

.1348 

557 

54 

7 

860 

767 

.2338 

272 

53 

7 

446 

879 

.1332 

545 

53 

8 

886 

802 

.2320 

260 

52 

8 

473 

914 

.1315 

532 

52 

9 

913 

837 

.2303 

248 

51 

9 

499 

950 

.1299 

520 

51 

10 

.40939 

.44872 

2.2286 

.91236 

50 

10 

.42525 

.46985 

2.1283 

.90507 

50 

11 

966 

907 

.2268 

224 

49 

11 

552 

.47021 

.1267 

495 

49 

12 

.40992 

942 

.2251 

212 

48 

12 

578 

056 

.1251 

483 

48 

13 

.41019 

.44977 

.2234 

200 

47 

13 

604 

092 

.1235 

470 

47 

14 

045 

.45012 

.2216 

188 

46 

14 

631 

128 

.1219 

458 

46 

15 

.41072 

.45047 

2.2199 

.91176 

45 

15 

.42657 

.47163 

2.1203 

.90446 

45 

16 

098 

082 

.2182 

164 

44 

16 

683 

199 

.1187 

433 

44 

17 

125 

117 

.2165 

152 

43 

17 

709 

234 

.1171 

421 

43 

18 

151 

152 

.2148 

140 

42 

18 

736 

270 

.1155 

408 

42 

19 

178 

187 

.2130 

128 

41 

19 

762 

305 

.1139 

396 

41 

20 

.41204 

.45222 

2.2113 

.91116 

40 

20 

.42788 

.47341 

2.1123 

.90383 

40 

21 

231 

257 

.2096 

104 

39 

21 

815 

377 

.1107 

371 

39 

22 

257 

292 

.2079 

092 

38 

22 

841 

412 

.1092 

358 

38 

23 

284 

327 

.2062 

080 

37 

23 

867 

448 

.1076 

346 

37 

24 

310 

362 

.2045 

068 

36 

24 

894 

483 

.1060 

334 

36 

25 

.41337 

.45397 

2.2028 

.91056 

35 

25 

.42920 

.47519 

2.1044 

.90321 

35 

2G 

363 

432 

.2011 

044 

34 

26 

946 

555 

.1028 

309 

34 

27 

390 

467 

.1994 

032 

33 

27 

972 

590 

.1013 

296 

33 

28 

416 

502 

.1977 

020 

32 

28 

.42999 

626 

.0997 

284 

32 

29 

443 

538 

.1960 

.91008 

31 

29 

.43025 

662 

.0981 

271 

31 

30 

.41469 

.45573 

2.1943 

.90996 

30 

30 

.43051 

.47698 

2.0965 

.90259 

30 

31 

496 

608 

.1926 

984 

29 

31 

077 

733 

.0950 

246 

29 

32 

522 

643 

.1909 

972 

28 

32 

104 

769 

.0934 

233 

28 

33 

549 

678 

.1892 

960 

27 

33 

130 

805 

.0918 

221 

27 

34 

575 

713 

.1876 

948 

26 

34 

156 

840 

.0903 

208 

26 

35 

.41602 

.45748 

2.1859 

.90936 

25 

35 

.43182 

.47876 

2.0887 

.90196 

25 

36 

628 

784 

.1842 

924 

24 

36 

209 

912 

.0872 

183 

24 

37 

655 

819 

.1825 

911 

23 

37 

235 

948 

.0856 

171 

23 

38 

681 

854 

.1808 

899 

22 

38 

261 

.47984 

.0840 

158 

22 

39 

707 

889 

.1792 

887 

21 

39 

287 

.48019 

.0825 

146 

21 

40 

.41734 

.45924 

2.1775 

.90875 

20 

40 

.43313 

.48055 

2.0809 

.90133 

20 

41 

760 

960 

.1758 

863 

19 

41 

340 

091 

.0794 

120 

19 

42 

787 

.45995 

.1742 

851 

18 

42 

366 

127 

.0778 

108 

18 

43 

813 

.46030 

.1725 

839 

17 

43 

392 

163 

.0763 

095 

17 

44 

840 

065 

.1708 

826 

16 

44 

418 

198 

.0748 

082 

16 

45 

.41866 

.46101 

2.1692 

.90814 

15 

45 

.43445 

.48234 

2.0732 

.90070 

15 

46 

892 

136 

.1675 

802 

14 

46 

471 

270 

.0717 

057 

14 

47 

919 

171 

.1659 

790 

13 

47 

497 

306 

.0701 

045 

13 

48 

945 

206 

.1642 

778 

12 

48 

523 

342 

.0686 

032 

12 

49 

972 

242 

.1625 

766 

11 

49 

549 

378 

.0671 

019 

11 

50 

.41998 

.46277 

2.1609 

.90753 

10 

50 

.43575 

.48414 

2.0655 

.90007 

10 

51 

.42024 

312 

.1592 

741 

9 

51 

602 

450 

.0640 

.89994 

9 

52 

051 

348 

.1576 

729 

8 

52 

628 

486 

.0625 

981 

8 

53 

077 

383 

.1560 

717 

7 

53 

654 

521 

.0609 

968 

7 

54 

104 

418 

.1543 

704 

6 

54 

680 

557 

.0594 

956 

6 

55 

.42130 

.46454 

2.1527 

.90692 

5 

55 

.43706 

.48593 

2.0579 

.89943 

5 

56 

156 

489 

.1510 

680 

4 

56 

733 

629 

.0564 

930 

4 

57 

183 

525 

.1494 

668 

3 

57 

759 

665 

.0549 

918 

3 

58 

209 

560 

.1478 

655 

2 

58 

785 

701 

.0533 

905 

2 

59 

235 

595 

.1461 

643 

1 

59 

811 

737 

.0518 

892 

1 

60 

.42262 

.46631 

2.1445 

.90631 

0 

60 

.43837 

.48773 

2.0503 

.89879 

0 

Cos 

Ctn 

Tan 

Sin 

/ 

Cos 

Ctn 

Tan 

Sin 

/ 

65C 


II]          26°  —  Values  of  Trigonometric  Functions 


35 


t 

Sin 

Tan 

Ctn 

Cos 

' 

Sin 

Tan 

Ctn 

Cos 

0 

.43837 

.48773 

2.0503 

.89879 

60 

0 

.45399 

.50953 

1.9626 

.89101 

60 

1 

863 

809 

.0488 

867 

59 

1 

425 

.50989 

.9612 

087 

59 

2 

889 

845 

.0473 

854 

58 

2 

451 

.51026 

.9598 

074 

58 

3 

916 

881 

.0458 

841 

57 

3 

477 

063 

.9584 

061 

57 

4 

942 

917 

.0443 

828 

56 

4 

503 

099 

.9570 

048 

56 

5 

.43968 

.48953 

2.0428 

.89816 

55 

5 

.45529 

.51136 

1.9556 

.89035 

55 

6 

.43994 

.48989 

.0413 

803 

54 

6 

554 

173 

.9542 

021 

54 

7 

.44020 

.49026 

.0398 

790 

53 

7 

580 

209 

.9528 

.89008 

53 

8 

046 

062 

.0383 

777 

52 

8 

606 

246 

.9514 

.88995 

52 

9 

072 

098 

.0368 

764 

51 

9 

632 

283 

.9500 

981 

51 

10 

.44098 

.49134 

2.0353 

.89752 

50 

10 

.45658 

.51319 

1.9486 

.88968 

50 

11 

124 

170 

.0338 

739 

49 

11 

684 

356 

.9472 

955 

49 

12 

151 

206 

.0323 

726 

48 

12 

710 

393 

.9458 

942 

48 

13 

177 

242 

.0308 

713 

47 

13 

736 

430 

.9444 

928 

47 

14 

203 

278 

.0293 

700 

46 

14 

762 

467 

.9430 

915 

46 

15 

.44229 

.49315 

2.0278 

.89687 

45 

15 

.45787 

.51503 

1.9416 

.88902 

45 

16 

255 

351 

.0263 

674 

44 

16 

813 

540 

.9402 

888 

44 

17 

281 

387 

.0248 

662 

43 

17 

839 

577 

.9388 

875 

43 

18 

307 

423 

.0233 

649 

42 

18 

865 

614 

.9375 

862 

42 

19 

333 

459 

.0219 

636 

41 

19 

891 

651 

.9361 

848 

41 

20 

.44359 

.49495 

2.0204 

.89623 

40 

20 

.45917 

.51688 

1.9347 

.88835 

40 

21 

385 

532 

.0189 

610 

39 

21 

942 

724 

.9333 

822 

39 

22 

411 

568 

.0174 

597 

38 

22 

968 

761 

.9319 

808 

38 

23 

437 

604 

.0160 

584 

37 

23 

.45994 

798 

.9306 

795 

37 

24 

464 

640 

.0145 

571 

36 

24 

.46020 

835 

.9292 

782 

36 

25 

.44490 

.49677 

2.0130 

.89558 

35 

25 

.46046 

.51872 

1.9278 

.88768 

35 

26 

516 

713 

.0115 

545 

34 

26 

072 

909 

.9265 

755 

34 

27 

542 

749 

.0101 

532 

33 

27 

097 

946 

.9251 

741 

33 

28 

568 

786 

.0086 

519 

32 

28 

123 

.51983 

.9237 

728 

32 

29 

594 

822 

.0072 

506 

31 

29 

149 

.52020 

.9223 

715 

31 

30 

.44620 

.49858 

2.0057 

.89493 

30 

30 

.46175 

.52057 

1.9210 

.88701 

30 

31 

646 

894 

.0042 

480 

29 

31 

201 

094 

.9196 

688 

29 

32 

672 

931 

.0028 

467 

28 

32 

226 

131 

.9183 

674 

28 

33 

698 

.49967 

2.0013 

454 

27 

33 

252 

168 

.9169 

661 

27 

34 

724 

.50004 

^9999 

441 

26 

34 

278 

205 

.9155 

647 

26 

35 

.44750 

.50040 

1.9984 

.89428 

25 

35 

.46304 

.52242 

1.9142 

.88634 

25 

36 

776 

076 

.9970 

415 

24 

36 

330 

279 

.9128 

620 

24 

37 

802 

113 

.9955 

402 

23 

37 

355 

316 

.9115 

607 

23 

38 

828 

149 

.9941 

389 

22 

38 

381 

353 

.9101 

593 

22 

39 

854 

185 

.9926 

376 

21 

39 

407 

390 

.9088 

580 

21 

40 

.44880 

.50222 

1.9912 

.89363 

20 

40 

.46433 

.52427 

1.9074 

.88566 

20 

41 

906 

258 

.9897 

350 

19 

41 

458 

464 

.9061 

553 

19 

42 

932 

295 

.9883 

337 

18 

42 

484 

501 

.9047 

539 

18 

43 

958 

331 

.9868 

324 

17 

43 

510 

538 

.9034 

526 

17 

44 

.44984 

368 

.9854 

311 

16 

44 

536 

575 

.9020 

512 

16 

45 

.45010 

.50404 

1.9840 

.89298 

15 

45 

.46561 

.52613 

1.9007 

.88499 

15 

46 

036 

441 

.9825 

285 

14 

46 

587 

650 

.8993 

485 

14 

47 

062 

477 

.9811 

272 

13 

47 

613 

687 

.8980 

472 

13 

48 

088 

514 

.9797 

259 

12 

48 

639 

724 

.8967 

458 

12 

49 

114 

550 

.9782 

245 

11 

49 

664 

761 

.8953 

445 

11 

50 

.45140 

.50587 

1.9768 

.89232 

10 

50 

.46690 

.52798 

1.8940 

.88431 

10 

51 

166 

623 

.9754 

219 

9 

51 

716 

836 

.8927 

417 

9 

52 

192 

660 

.9740 

206 

8 

52 

742 

873 

.8913 

404 

8 

53 

218 

696 

.9725 

193 

7 

53 

767 

910 

.8900 

390 

7 

54 

243 

733 

.9711 

180 

6 

54 

793 

947 

.8887 

377 

6 

55 

.45269 

.50769 

1.9697 

.89167 

5 

55 

.46819 

.52985 

1.8873 

.88363 

5 

56 

295 

806 

.9683 

153 

4 

56 

844 

.53022 

.8860 

349 

4 

57 

321 

843 

.9669 

140 

3 

57 

870 

059 

.8847 

336 

3 

58 

347 

879 

.9654 

127 

2 

58 

.896 

096 

.8834 

322 

2 

59 

373 

916 

.9640 

114 

1 

59 

921 

134 

.8820 

308 

1 

60 

.45399 

.50953 

1.9626 

.89101 

0 

60 

.46947 

.53171 

1.8807 

.88295 

0 

Cos 

Ctn   Tan 

Sin 

/ 

Cos   Ctn 

Tan 

Sin 

1 

63C 


62C 


36 


28°  —  Values  of  Trigonometric  Functions  —  29e 


/ 

Sin 

Tan 

Ctn 

Cos 

i 

Sin 

Tan 

Ctn 

Cos 

0 

.46947 

.53171 

1.8807 

.88295 

60 

0 

.48481 

.55431 

1.8040 

.87462 

60 

1 

973 

208 

.8794 

281 

59 

1 

506 

469 

.8028 

448 

59 

2 

.46999 

246 

.8781 

267 

58 

2 

532 

507 

.8016 

434 

58 

3 

.47024 

283 

.8768 

254 

57 

3 

557 

545 

.8003 

420 

57 

4 

050 

320 

.8755 

240 

56 

4 

583 

583 

.7991 

406 

56 

5 

.47076 

.53358 

1.8741 

.88226 

55 

5 

.48608 

.55621 

1.7979 

.87391 

55 

6 

101 

395 

.8728 

213 

54 

6 

634 

659 

.7966 

377 

54 

7 

127 

432 

.8715 

199 

53 

7 

659 

697 

.7954 

363 

53 

8 

153 

470 

.8702 

185 

52 

8 

684 

736 

.7942 

349 

52 

9 

178 

507 

.8689 

172 

51 

9 

710 

774 

.7930 

335 

51 

10 

.47204 

.53545 

1.8676 

.88158 

50 

10 

.48735 

.55812 

1.7917 

.87321 

50 

11 

229 

582 

.8663 

144 

49 

11 

761 

850 

.7905 

306 

49 

12 

255 

620 

.8650 

130 

48 

12 

786 

888 

.7893 

292 

48 

13 

281 

657 

.8637 

117 

47 

13 

811 

926 

.7881 

278 

47 

14 

306 

694 

.8624 

103 

46 

14 

837 

.55964 

.7868 

264 

46 

15 

.47332 

.53732 

1.8611 

.88089 

45 

15 

.48862 

.56003 

1.7856 

.87250 

45 

16 

358 

769 

.8598 

075 

44 

16 

888 

041 

.7844 

235 

44 

17 

383 

807 

.8585 

062 

43 

17 

913 

079 

.7832 

221 

43 

18 

409 

844 

.8572 

048 

42 

18 

938 

117 

.7820 

207 

42 

19 

434 

882 

.8559 

034 

41 

19 

964 

156 

.7808 

193 

41 

20 

.47460 

.53920 

1.8546 

.88020 

40 

20 

.48989 

.56194 

1.7796 

.87178 

40 

21 

486 

957 

.8533 

.88006 

39 

21 

.49014 

232 

.7783 

164 

39 

22 

511 

.53995 

.8520 

.87993 

38 

22 

040 

270 

.7771 

150 

38 

23 

537 

.54032 

.8507 

979 

37 

23 

065 

309 

.7759 

136 

37 

24 

562 

070 

.8495 

965 

36 

24 

090 

347 

.7747 

121 

36 

25 

.47588 

.54107 

1.8482 

.87951 

35 

25 

.49116 

.56385 

1.7735 

.87107 

35 

26 

614 

145 

.8469 

937 

34 

26 

141 

424 

.7723 

093 

34 

27 

639 

183 

.8456 

923 

33 

27 

166 

462 

.7711 

079 

33 

28 

665 

220 

.8443 

909 

32 

28 

192 

501 

.7699 

064 

32 

29 

690 

258 

.8430 

896 

31 

29 

217 

539 

.7687 

050 

31 

30 

.47716 

.54296 

1.8418 

.87882 

30 

30 

.49242 

.56577 

1.7675 

.87036 

30 

31 

741 

333 

.8405 

868 

29 

31 

268 

616 

.7663 

021 

29 

32 

767 

371 

.8392 

854 

28 

32 

293 

654 

.7651 

.87007 

28 

33 

793 

409 

.8379 

840 

27 

33 

318 

693 

.7639 

.86993 

27 

34 

818 

446 

.8367 

826 

26 

34 

344 

731 

.7627 

978 

26 

35 

.47844 

.54484 

1.8354 

.87812 

25 

35 

.49369 

.56769 

1.7615 

.86964 

25 

36 

869 

522 

.8341 

798 

24 

36 

394 

808 

.7603 

949 

24 

37 

895 

560 

.8329 

784 

23 

37 

419 

846 

.7591 

935 

23 

38 

920 

597 

.8316 

770 

22 

38 

445 

885 

.7579 

921 

22 

39 

946 

635 

.8303 

756 

21 

39 

470 

923 

.7567 

906 

21 

40 

.47971 

.54673 

1.8291 

.87743 

20 

40 

.49495 

.56962 

1.7556 

.86892 

20 

41 

.47997 

711 

.8278 

729 

19 

41 

521 

.57000 

.7544 

878 

19 

42 

.48022 

748 

.8265 

715 

18 

42 

546 

039 

.7532 

863 

18 

43 

048 

786 

.8253 

701 

17 

43 

571 

078 

.7520 

849 

17 

44 

073 

824 

.8240 

687 

16 

44 

596 

116 

.7508 

834 

16 

45 

.48099 

.54862 

1.8228 

.87673 

15 

45 

.49622 

.57155 

1.7496 

.86820 

15 

46 

124 

900 

.8215 

659 

14 

46 

647 

193 

.7485 

805 

14 

47 

150 

938 

.8202 

645 

13 

47 

672 

232 

.7473 

791 

13 

48 

175 

.54975 

.8190 

631 

12 

48 

697 

271 

.7461 

111 

12 

49 

201 

.55013 

.8177 

617 

11 

49 

723 

309 

.7449 

762 

11 

50 

.48226 

.55051 

1.8165 

.87603 

10 

50 

.49748 

.57348 

1.7437 

.86748 

10 

51 

252 

089 

.8152 

589 

9 

51 

773 

386 

.7426 

733 

9 

52 

277 

127 

.8140 

575 

8 

52 

798 

425 

.7414 

719 

8 

53 

303 

165 

.8127 

561 

7 

53 

824 

464 

.7402 

704 

7 

54 

328 

203 

.8115 

546 

6 

54 

849 

503 

.7391 

690 

6 

55 

.48354 

.55241 

1.8103 

.87532 

5 

55 

.49874 

.57541 

1.7379 

.86675 

5 

56 

379 

279 

.8090 

518 

4 

56 

899 

580 

.7367 

661 

4 

57 

405 

317 

.8078 

504 

3 

57 

924 

619 

.7355 

646 

3 

58 

430 

355 

.8065 

490 

2 

58 

950 

657 

.7344 

632 

2 

59 

456 

393 

.8053 

476 

1 

59 

.49975 

696 

.7332 

617 

1 

60 

.48481 

.55431 

1.8040 

.87462 

0 

60 

.50000 

.57735 

1.7321 

.86603 

_0 

Cos 

Ctn 

Tan 

Sin 

i 

Cos 

Ctn 

Tan 

Sin 

i 

61C 


60C 


II]          30°  —  Values  of  Trigonometric  Functions  —  31C 


37 


' 

Sin 

Tan 

Ctn 

Cos 

/ 

Sin 

Tan 

Ctn 

Cos 

0 

.50000 

.57735 

1.7321 

.86603 

60 

0 

.51504 

.60086 

1.6643 

.85717 

60 

1 

025 

774 

.7309 

588 

59 

1 

529 

126 

.6632 

702 

59 

2 

050 

813 

.7297 

573 

58 

2 

554 

165 

.6621 

687 

58 

3 

076 

851 

.7286 

559 

57 

3 

579 

205 

.6610 

672 

57 

4 

101 

890 

.7274 

544 

56 

4 

604 

245 

.6599 

657 

56 

5 

.50126 

.57929 

1.7262 

.86530 

55 

5 

.51628 

.60284 

1.6588 

.85642 

55 

6 

151 

.57968 

.7251 

515 

54 

6 

653 

324 

.6577 

627 

54 

7 

176 

.58007 

.7239 

501 

53 

7 

678 

364 

.6566 

612 

53 

8 

201 

046 

.7228 

486 

52 

8 

703 

403 

.6555 

597 

52 

9 

227 

085 

.7216 

471 

51 

9 

728 

443 

.6545 

582 

51 

10 

.50252 

.58124 

1.7205 

.86457 

50 

10 

.51753 

.60483 

1.6534 

.85567 

50 

11 

277 

162 

.7193 

442 

49 

11 

778 

522 

.6523 

551 

49 

12 

302 

201 

.7182 

427 

48 

12 

803 

562 

.6512 

536 

48 

13 

327 

240 

.7170 

413 

47 

13 

828 

602 

.6501 

521 

47 

14 

352 

279 

.7159 

398 

46 

14 

852 

642 

.6490 

506 

46 

15 

.50377 

.58318 

1.7147 

.86384 

45 

15 

.51877 

.60681 

1.6479 

.85491 

45 

16 

403 

357 

.7136 

369 

44 

16 

902 

721 

.6469 

476 

44 

17 

428 

396 

.7124 

354 

43 

17 

927 

761 

.6458 

461 

43 

18 

453 

435 

.7113 

340 

42 

18 

952 

801 

.6447 

446 

42 

19 

478 

474 

.T102 

325 

41 

19 

.51977 

841 

.6436 

431 

41 

20 

.50503 

.58513 

1.7090 

.86310 

40 

20 

.52002 

.60881 

1.6426 

.85416 

40 

21 

528 

552 

.7079 

295 

39 

21 

026 

921 

.6415 

401 

39 

22 

553 

591 

.7067 

281 

38 

22 

051 

.60960 

.6404 

385 

38 

23 

578 

631 

.7056 

266 

37 

23 

076 

.61000 

.6393 

370 

37 

24 

603 

670 

.7045 

251 

36 

24 

101 

040 

.6383 

355 

36 

25 

.50628 

.58709 

1.7033 

.86237 

35 

25 

.52126 

.61080 

1.6372 

.85340 

35 

26 

654 

748 

.7022 

222 

34 

26 

151 

120 

.6361 

325 

34 

27 

679 

787 

.7011 

207 

33 

27 

175 

160 

.6351 

310 

33 

28 

704 

826 

.6999 

192 

32 

28 

200 

200 

.6340 

294 

32 

29 

729 

865 

.6988 

178 

31 

29 

225 

240 

.6329 

279 

31 

30 

.50754 

.58905 

1.6977 

.86163 

30 

30 

.52250 

.61280 

1.6319 

.85264 

30 

31 

779 

944 

.6965 

148 

29 

31 

275 

320 

.6308 

249 

29 

32 

804 

.58983 

.6954 

133 

28 

32 

299 

360 

.6297 

234 

28 

33 

829 

.59022 

.6943 

119 

27 

33 

324 

400 

.6287 

218 

27 

34 

854 

061 

.6932 

104 

26 

34 

349 

440 

.6276 

203 

26 

35 

.50879 

.59101 

1.6920 

.86089 

25 

35 

.52374 

.61480 

1.6265 

.85188 

25 

36 

904 

140 

.6909 

074 

24 

36 

399 

520 

.6255 

173 

24 

37 

929 

179 

.6898 

059 

23 

37 

423 

561 

.6244 

157 

23 

38 

954 

218 

.6887 

045 

22 

38 

448 

601 

.6234 

142 

22 

39 

.50979 

258 

.6875 

030 

21 

39 

473 

641 

.6223 

127 

21 

40 

.51004 

.59297 

1.6864 

.86015 

20 

40 

.52498 

.61681 

1.6212 

.85112 

20 

41 

029 

336 

.6853 

.86000 

19 

41 

522 

721 

.6202 

096 

19 

42 

054 

376 

.6842 

.85985 

18 

42 

547 

761 

.6191 

081 

18 

43 

079 

415 

.6831 

970 

17 

43 

572 

801 

.6181 

066 

17 

44 

104" 

454 

.6820 

956 

16 

44 

597 

842 

.6170 

051 

16 

45 

.51129 

.59494 

1.6808 

.85941 

15 

45 

.52621 

.61882 

1.6160 

.85035 

15 

46 

154 

533 

.6797 

926 

14 

46 

646 

922 

.6149 

020 

14 

47 

179 

573 

.6786 

911 

13 

47 

671 

.61962 

.6139 

.85005 

13 

48 

204 

612 

.6775 

896 

12 

48 

696 

.62003 

.6128 

.84989 

12 

49 

229 

651 

.6764 

881 

11 

49 

720 

043 

.6118 

974 

11 

50 

.51254 

.59691 

1.6753 

.85866 

10 

50 

.52745 

.62083 

1.6107 

.84959 

10 

51 

279 

730 

.6742 

851 

9 

51 

770 

124 

.6097 

943 

9 

52 

304 

770 

.6731 

836 

8 

52 

794 

164 

.6087 

928 

8 

53 

320 

809 

.6720 

821 

7 

53 

819 

204 

.6076 

913 

7 

54 

354 

849 

.6709 

806 

6 

54 

844 

245 

.6066 

897 

6 

55 

.51379 

.59888 

1.6698 

.85792 

5 

55 

.52869 

.62285 

1.6055 

.84882 

5 

56 

404 

928 

.6687 

111 

4 

56 

893 

325 

.6045 

866 

4 

57 

429 

.59967 

.6676 

762 

3 

57 

918 

366 

.6034 

851 

3 

58 

454 

.60007 

.6665 

747 

2 

58 

943 

406 

.6024 

836 

2 

59 

479 

046 

.6654 

732 

1 

59 

967 

446 

.6014 

820 

1 

60 

.51504 

.60086 

1.6643 

.85717 

0 

60 

.52992 

.62487 

1.6003 

.84805 

0 

Cos 

Ctn   Tan 

Sin 

/ 

Cos 

Ctn 

Tan 

Sin 

/ 

59° 


58C 


38 


32°  —  Values  of  Trigonometric  Functions  —  33C 


/ 

Sin 

Tan 

Ctn 

Cos 

/ 

Sin 

Tan 

Ctn 

Cos 

0 

.52992 

.62487 

1.6003 

.84805 

60 

0 

.54464 

.64941 

1.5399 

.83867 

60 

1 

.53017 

527 

.5993 

789 

59 

1 

488 

.64982 

.5389 

851 

59 

2 

041 

568 

.5983 

774 

58 

2 

513 

.65024 

.5379 

835 

58 

3 

066 

608 

.5972 

759 

57 

3 

537 

065 

.5369 

819 

57 

4 

091 

649 

.5962 

743 

56 

4 

561 

106 

.5359 

804 

56 

5 

.53115 

.62689 

1.5952 

.84728 

55 

5 

.54586 

.65148 

1.5350 

.83788 

55 

6 

140 

730 

.5941 

712 

54 

6 

610 

189 

.5340 

111 

54 

7 

164 

770 

.5931 

697 

53 

7 

635 

231 

.5330 

756 

53 

8 

189 

811 

.5921 

681 

52 

8 

659 

272 

.5320 

740 

52 

9 

214 

852 

.5911 

666 

51 

9 

683 

314 

.5311 

724 

51 

10 

.53238 

.62892 

1.5900 

.84650 

50 

10 

.54708 

.65355 

1.5301 

.83708 

50 

11 

263 

933 

.5890 

635 

49 

11 

732 

397 

.5291 

692 

49 

12 

288 

.62973 

.5880 

619 

48 

12 

756 

438 

.5282 

676 

48 

13 

312 

.63014 

.5869 

604 

47 

13 

781 

480 

.5272 

660 

47 

14 

337 

055 

.5859 

588 

46 

14 

805 

521 

.5262 

645 

46 

15 

.53361 

.63095 

1.5849 

.84573 

45 

15 

.54829 

.65563 

1.5253 

.83629 

45 

16 

386 

136 

.5839 

557 

44 

16 

854 

604 

.5243 

613 

44 

17 

411 

177 

.5829 

542 

43 

17 

878 

646 

.5233 

597 

43 

18 

435 

217 

.5818 

526 

42 

18 

902 

688 

.5224 

581 

42 

19 

460 

258 

.5808 

511 

41 

19 

927 

729 

.5214 

565 

41 

20 

.53484 

.63299 

1.5798 

.84495 

40 

20 

.54951 

.65771 

1.5204 

.83549 

40 

21 

509 

340 

.5788 

480 

39 

21 

975 

813 

.5195 

533 

39 

22 

534 

380 

.5778 

464 

38 

22 

.54999 

854 

.5185 

517 

38 

23 

558 

421 

.5768 

448 

37 

23 

.55024 

896 

.5175 

501 

37 

24 

583 

462 

.5757 

433 

36 

24 

048 

938 

.5166 

485 

36 

25 

.53607 

.63503 

1.5747 

.84417 

35 

25 

.55072 

.65980 

1.5156 

.83469 

35 

26 

632 

544 

.5737 

402 

34 

26 

097 

.66021 

.5147 

453 

34 

27 

656 

584 

.5727 

386 

33 

27 

121 

063 

.5137 

437 

33 

28 

681 

625 

.5717 

370 

32 

28 

145 

105 

.5127 

421 

32 

29 

705 

666 

.5707 

355 

31 

29 

169 

147 

.5118 

405 

31 

30 

.53730 

.63707 

1.5697 

.84339 

30 

30 

.55194 

.66189 

1.5108 

.83389 

30 

31 

754 

748 

.5687 

324 

29 

31 

218 

230 

.5099 

373 

29 

32 

779 

789 

.5677 

308. 

28 

32 

242 

272 

.5089 

356 

28 

33 

804 

830 

.5667 

292 

27 

33 

266 

314 

.5080 

340 

27 

34 

828 

871 

.5657 

277 

26 

34 

291 

356 

.5070 

324 

26 

35 

.53853 

.63912 

1.5647 

.84261 

25 

35 

.55315 

.66398 

1.5061 

.83308 

25 

30 

877 

953 

.5637 

245 

24 

36 

339 

440 

.5051 

292 

24 

37 

902 

.63994 

.5627 

230 

23 

37 

363 

482 

.5042 

276 

23 

38 

926 

.64035 

.5617 

214 

22 

38 

388 

524 

.5032 

260 

22 

39 

951 

076 

.5607 

198 

21 

39 

412 

566 

.5023 

244 

21 

40 

.53975 

.64117 

1.5597 

.84182 

20 

40 

.55436 

.66608 

1.5013 

.83228 

20 

41 

.54000 

158 

.5587 

167 

19 

41 

460 

650 

.5004 

212 

19 

42 

024 

199 

.5577 

151 

18 

42 

484 

692 

.4994 

195 

18 

43 

049 

240 

.5567 

135 

17 

43 

509 

734 

.4985 

179 

17 

44 

073 

281 

.5557 

120 

16 

44 

533 

776 

.4975 

163 

16 

45 

.54097 

.64322 

1.5547 

.84104 

15 

45 

.55557 

.66818 

1.4966 

.83147 

15 

46 

122 

363 

.5537 

088 

14 

46 

581 

860 

.4957 

131 

14 

47 

146 

404 

.5527 

072 

13 

47 

605 

902 

.4947 

115 

13 

48 

171 

446 

.5517 

057 

12 

48 

630 

944 

.4938 

098 

12 

49 

195 

487 

.5507 

041 

11 

49 

65~4 

.66986 

.4928 

082 

11 

50 

.54220 

.64528 

1.5497 

.84025 

10 

50 

.55678 

.67028 

1.4919 

.83066 

10 

51 

244 

569 

.5487 

.84009 

9 

51 

702 

071 

.4910 

050 

9 

52 

269 

610 

.5477 

.83994 

8 

52 

726 

113 

.4900 

034 

8 

53 

293 

652 

.5468 

978 

7 

53 

750 

155 

.4891 

017 

7 

54 

317 

693 

.5458 

962 

& 

54 

775 

197 

.4882 

.83001 

6 

55 

.54342 

.64734 

1.5448 

.83946 

5 

55 

.55799 

.67239 

1.4872 

.82985 

5 

56 

366 

775 

.5438 

930 

4 

56 

823 

282 

.4863 

969 

4 

57 

391 

817 

.5428 

915 

3 

57 

847 

324 

.4854 

953 

3 

58 

415 

858 

.5418 

899 

2 

58 

871 

366 

.4844 

936 

2 

59 

440 

899 

.5408 

883 

1 

59 

895 

409 

.4835 

920 

1 

60 

.54464 

.64941 

1.5399 

.83867 

0 

60 

.55919 

.67451 

1.4826 

.82904 

0 

Cos 

Ctn 

Tan 

Sin 

/ 

Cos 

Ctn 

Tan 

Sin 

/ 

57C 


56C 


II]          34°  —  Values  of  Trigonometric  Functions  —  35e 


/ 

Sin 

Tan 

Ctn 

Cos 

/ 

Sin 

Tan 

Ctn 

Cos 

0 

55919 

.67451 

1.4826 

.82904 

60 

0 

.57358 

.70021 

1.4281 

.81915 

60 

1 

943 

493 

.4816 

887 

59 

1 

381 

064 

.4273 

899 

59 

2 

968 

536 

.4807 

871 

58 

2 

405 

107 

.4264 

882 

58 

3 

55992 

578 

.4798 

855 

57 

3 

429 

151 

.4255 

865 

57 

4 

56016 

620 

.4788 

839 

56 

4 

453 

194 

.4246 

848 

56 

5 

56040 

.67663 

1.4779 

.82822 

55 

5 

.57477 

.70238 

1.4237 

.81832 

55 

6 

064 

705 

.4770 

806 

54 

6 

501 

281 

.4229 

815 

54 

7 

088 

748 

.4761 

790 

53 

7 

524 

325 

.4220 

798 

53 

8 

112 

790 

.4751 

773 

52 

8 

548 

368 

.4211 

782 

52 

9 

136 

832 

.4742 

757 

51 

9 

572 

412 

.4202 

765 

51 

10 

56160 

.67875 

1.4733 

.82741 

50 

10 

.57596 

.70455 

1.4193 

.81748 

50 

11 

184 

917 

.4724 

724 

49 

11 

619 

499 

.4185 

731 

49 

12 

208 

.67960 

.4715 

708 

48 

12 

643 

542 

.4176 

714 

48 

13 

232 

.68002 

.4705 

692 

47 

13 

667 

586 

.4167 

698 

47 

14 

256 

045 

.4696 

675 

46 

14 

691 

629 

.4158 

681 

46 

15 

.56280 

.68088 

1.4687 

.82659 

45 

15 

.57715 

.70673 

1.4150 

.81664 

45 

16 

305 

130 

.4678 

643 

44 

16 

738 

717 

.4141 

647 

44 

17 

329 

173 

.4669 

626 

43 

17 

762 

760 

.4132 

631 

43 

18 

353 

215 

.4659 

610 

42 

18 

786 

804 

.4124 

614 

42 

19 

377 

258 

.4650 

593 

41 

19 

810 

848 

.4115 

597 

41 

20 

.56401 

.68301 

1.4641 

.82577 

40 

20 

.57833 

.70891 

1.4106 

.81580 

40 

21 

425 

343 

.4632 

561 

39 

21 

857 

935 

.4097 

563 

39 

22 

449 

386 

.4623 

544 

38 

22 

881 

.70979 

.4089 

546 

38 

23 

473 

429 

.4614 

528 

37 

23 

904 

.71023 

.4080 

530 

37 

24 

497 

471 

.4605 

511 

36 

24 

928 

066 

.4071 

513 

36 

25 

.56521 

.68514 

1.4596 

.82495 

35 

25 

.57952 

.71110 

1.4063 

.81496 

35 

26 

545 

557 

.4586 

478 

34 

26 

976 

154 

.4054 

479 

34 

27 

569 

600 

.4577 

462 

33 

27 

.57999 

198 

.4045 

462 

33 

28 

593 

642 

.4568 

446 

32 

28 

.58023 

242 

.4037 

445 

32 

29 

617 

685 

.4559 

429 

31 

29 

047 

285 

.4028 

428 

31 

30 

.56641 

.68728 

1.4550 

.82413 

30 

30 

.58070 

.71329 

1.4019 

.81412 

30 

31 

665 

771 

.4541 

396 

29 

31 

094 

373 

.4011 

395 

29 

32 

689 

814 

.4532 

380 

28 

32 

118 

417 

.4002 

378 

28 

33 

713 

857 

.4523 

363 

27 

33 

141 

461 

.3994 

361 

27 

34 

736 

900 

.4514 

347 

26 

34 

165 

505 

.3985 

344 

26 

35 

.56760 

.68942 

1.4505 

.82330 

25 

35 

.58189 

.71549 

1.3976 

.81327 

25 

36 

784 

.68985 

.4496 

314 

24 

36 

212 

593 

.3968 

310 

24 

37 

808 

.69028 

.4487 

297 

23 

37 

236 

637 

.3959 

293 

23 

38 

832 

071 

.4478 

281 

22 

38 

260 

681 

.3951 

276 

22 

39 

856 

114 

.4469 

264 

21 

39 

283 

725 

.3942 

259 

21 

40 

.56880 

.69157 

1.4460 

.82248 

20 

40 

.58307 

.71769 

1.3934 

.81242 

20 

41 

904 

200 

.4451 

231 

19 

41 

330 

813 

.3925 

225 

19 

42 

928 

243 

.4442 

214 

18 

42 

354 

857 

.3916 

208 

18 

43 

952 

286 

.4433 

198 

17 

43 

378 

901 

.3908 

191 

17 

44 

.56976 

329 

.4424 

181 

16 

44 

401 

946 

.3899 

174 

16 

45 

.57000 

.69372 

1.4415 

.82165 

15 

45 

.58425 

.71990 

1.3891 

.81157 

15 

46 

024 

416 

.4406 

148 

14 

46 

449 

.72034 

.3882 

140 

14 

47 

047 

459 

.4397 

132 

13 

47 

472 

078 

.3874 

123 

13 

48 

071 

502 

.4388 

115 

12 

48 

496 

122 

.3865 

106 

12 

49 

095 

545 

.4379 

098 

11 

49 

519 

167 

.3857 

089 

11 

50 

.57119 

.69588 

1.4370 

.82082 

10 

50 

.58543 

.72211 

1.3848 

.81072 

10 

51 

143 

631 

.4361 

065 

9 

51 

567 

255 

.3840 

055 

9 

52 

167 

675 

.4352 

048 

8 

52 

590 

299 

.3831 

038 

8 

53 

191 

718 

.4344 

032 

7 

53 

614 

344 

.3823 

021 

7 

54 

215 

761 

.4335 

.82015 

6 

54 

637 

388 

.3814 

.81004 

6 

55 

.57238 

.69804 

1.4326 

.81999 

5 

55 

.58661 

.72432 

1.3806 

.80987 

5 

56 

262 

847 

.4317 

982 

4 

56 

684 

477 

.3798 

970 

4 

57 

286 

891 

.4308 

965 

3 

57 

708 

521 

.3789 

953 

3 

58 

310 

934 

.4299 

949 

2 

58 

731 

565 

.3781 

936 

2 

59 

334 

.69977 

.4290 

932 

1 

59 

755 

610 

.3772 

919 

1 

60 

.57358 

.70021 

1.4281 

.81915 

0 

60 

.58779 

.72654 

1.3764 

.80902 

0 

Cos 

Ctn 

Tan 

Sin 

/ 

Cos 

Ctn 

Tan 

Sin 

' 

55C 


54C 


40 


36°  —  Values  of  Trigonometric  Functions  —  37C 


[II 


/ 

Sin 

Tan 

Ctn 

Cos 

/ 

Sin 

Tan 

Ctn 

Cos 

0 

.58779 

.72654 

1.3764 

.80902 

60 

0 

.60182 

.75355 

1.3270 

.79864 

60 

1 

802 

699 

.3755 

885 

59 

1 

205 

401 

.3262 

846 

59 

2 

826 

743 

.3747 

867 

58 

2 

228 

447 

.3254 

829 

58 

3 

849 

788 

.3739 

850 

57 

3 

251 

492 

.3246 

811 

57 

4 

873 

832 

.3730 

833 

56 

4 

274 

538 

.3238 

793 

56 

5 

.58896 

.72877 

1.3722 

.80816 

55 

5 

.60298 

.75584 

1.32.30 

.79776 

55 

6 

920 

921 

.3713 

799 

54 

6 

321 

629 

.3222 

758 

54 

7 

943 

.72966 

.3705 

782 

53 

7 

344 

675 

.3214 

741 

53 

8 

967 

.73010 

.3697 

765 

52 

8 

367 

721 

.3206 

723 

52 

9 

.58990 

055 

.3688 

748 

51 

9 

390 

767 

.3198 

706 

51 

10 

.59014 

.73100 

1.3680 

.80730 

50 

10 

.60414 

.75812 

1.3190 

.79688 

50 

11 

037 

144 

.3672 

713 

49 

11 

437 

858 

.3182 

671 

49 

12 

061 

189 

.3663 

696 

48 

12 

460 

904 

.3175 

653 

48 

13 

084 

234 

.3655 

679 

47 

13 

483 

950 

.3167 

635 

47 

14 

108 

278 

.3647 

662 

46 

14 

506 

.75996 

.3159 

618 

46 

15 

.59131 

.73323 

1.3638 

.80644 

45 

15 

.60529 

.76042 

1.3151 

.79600 

45 

16 

154 

368 

.3630 

627 

44 

16 

553 

088 

.3143 

583 

44 

17 

178 

413 

.3622 

610 

43 

17 

576 

134 

.3135 

565 

43 

18 

201 

457 

.3613 

593 

42 

18 

599 

180 

.3127 

547 

42 

19 

225 

502 

.3605 

"576 

41 

19 

622 

226 

.3119 

530 

41 

20 

.59248 

.73547 

1.3597 

.80558 

40 

20 

.60645 

.76272 

1.3111 

.79512 

40 

21 

272 

592 

.3588 

541 

39 

21 

668 

318 

.3103 

494 

39 

22 

295 

637 

.3580 

524 

38 

22 

691 

364 

.3095 

477 

38 

23 

318 

681 

.3572 

507 

37 

23 

714 

410 

.3087 

459 

37 

24 

342 

726 

.3564 

489 

36 

24 

738 

456 

.3079 

441 

36 

25 

.59365 

.73771 

1.3555 

.80472 

35 

25 

.60761 

.76502 

1.3072 

.79424 

35 

26 

389 

816 

.3547 

455 

34 

26 

784 

548 

.3064 

406 

34 

27 

412 

861 

.3539 

438 

33 

27 

807 

594 

.3056 

388 

33 

28 

436 

906 

.3531 

420 

32 

28 

830 

640 

.3048 

371 

32 

29 

459 

951 

.3522 

403 

31 

29 

853 

686 

.3040 

353 

31 

30 

.59482 

.73996 

1.3514 

.80386 

30 

30 

.60876 

.76733 

1.3032 

.79335 

30 

31 

506 

.74041 

.3506 

368 

29 

31 

899 

779 

.3024 

318 

29 

32 

529 

086 

.3498 

351 

28 

32 

922 

825 

.3017 

300 

28 

33 

552 

131 

.3490 

334 

27 

33 

945 

871 

.3009 

282 

27 

34 

576 

176 

.3481 

316 

26 

34 

968 

918 

.3001 

264 

26 

35 

.59599 

.74221 

1.3473 

.80299 

25 

35 

.60991 

.76964 

1.2993 

.79247 

25 

36 

622 

267 

.3465 

282 

24 

36 

.61015 

.77010 

.2985 

229 

24 

37 

646 

312 

.3457 

264 

23 

37 

038 

057 

.2977 

211 

23 

38 

669 

357 

.3449 

247 

22 

38 

061 

103 

.2970 

193 

22 

39 

693 

402 

.3440 

230 

21 

39 

084 

149 

.2962 

176 

2J 

40 

.59716 

.74447 

1.3432 

.80212 

20 

40 

.61107 

.77196 

1.2954 

.79158 

20 

41 

739 

492 

.3424 

195 

19 

41 

130 

242 

.2946 

140 

19 

42 

763 

538 

.3416 

178 

18 

42 

153 

289 

.2938 

122 

18 

43 

786 

583 

.3408 

160 

17 

43 

176 

335 

.2931 

105 

17 

44 

809 

628 

.3400 

143 

16 

44 

199 

382 

.2923 

087 

16 

45 

.59832 

.74674 

1.3392 

.80125 

15 

45 

.61222 

.77428 

1.2915 

.79069 

15 

46 

856 

719 

.3384 

108 

14 

46 

245 

475 

.2907 

051 

14 

47 

879 

764 

.3375 

091 

13 

47 

268 

521 

.2900 

033 

13 

48 

902 

810 

.3367 

073 

12 

48 

291 

568 

.2892 

.79016 

12 

49 

926 

855 

.3359 

056 

11 

49 

314 

615 

.2884 

.78998 

11 

50 

.59949 

.74900 

1.3351 

.80038 

10 

50 

.61337 

.77661 

1.2876 

.78980 

10 

51 

972 

946 

.3343 

021 

9 

51 

360 

708 

.2869 

962 

9 

52 

,59996 

.74991 

.3335 

.800(13 

& 

52 

383 

754 

.2861 

944 

8 

53 

.60019 

.75037 

.3327 

7799801 

7 

53 

406 

801 

.2853 

926 

7 

54 

042 

082 

.3319 

968 

G 

54 

429 

848 

.2846 

908 

6 

55 

.60065 

.75128 

1.3311 

.79951 

5 

55 

.61451 

.77895 

1.2838 

.78891 

5 

56 

089 

173 

.3303 

934 

4 

56 

474 

941 

.2830 

873 

4 

57 

112 

219 

.3295 

916 

3 

57 

497 

.77988 

.2822 

855 

3 

58 

135 

264 

.3287 

899 

2 

58 

520 

.78035 

.2815 

837 

2 

59 

158 

310 

.3278 

881 

1 

59 

543 

082 

.2807 

819 

1 

60 

.60182 

.75355 

1.3270 

.79864 

0 

60 

.61566 

.78129 

1.2799 

.78801 

_0_ 

Cos 

Ctn 

Tan 

Sin 

/ 

Cos 

Ctn 

Tan 

Sin 

/ 

53C 


52C 


II]          38°  —  Values  of  Trigonometric  Functions  —  39C 


41 


/ 

Sin 

Tan 

Ctn 

Cos 

/ 

Sin 

Tan 

Ctn 

Cos 

0 

.61566 

.78129 

1.2799 

.78801 

60 

0 

.62932 

.80978 

1.2349 

.77715 

60 

1 

589 

175 

.2792 

783 

59 

1 

955 

.81027 

.2342 

696 

59 

2 

612 

222 

.2784 

765 

58 

2 

.62977 

075 

.2334 

678 

58 

3 

635 

269 

.2776 

747 

57 

3 

.63000 

123 

.2327 

660 

57 

4 

658 

316 

.2769 

729 

56 

4 

022 

171 

.2320 

641 

56 

5 

.61681 

.78363 

1.2761 

.78711 

55 

5 

.63045 

.81220 

1.2312 

.77623 

55 

6 

704 

410 

.2753 

694 

54 

6 

068 

268 

.2305 

605 

54 

7 

726 

457 

.2746 

676 

53 

7 

090 

316 

.2298 

586 

53 

8 

749 

504 

.2738 

658 

52 

-s 

113 

364 

.2290 

568 

52 

9 

772 

551 

.2731 

640 

51 

9 

135 

413 

.2283 

550 

51 

10 

.61795 

.78598 

1.2723 

.78622 

50 

10 

.63158 

.81461 

1.2276 

.77531 

50 

11 

818 

645 

.2715 

604 

49 

11 

180 

510 

.2268 

513 

49 

12 

841 

692 

.2708 

586 

48 

12 

203 

558 

.2261 

494 

48 

13 

864 

739 

.2700 

568 

47 

13 

225 

606 

.2254 

476 

47 

14 

887 

786 

.2693 

550 

46 

14 

248 

655 

.2247 

458 

46 

15 

.61909 

.78834 

1.2685 

.78532 

45 

15 

.63271 

.81703 

1.2239 

.77439 

45 

16 

932 

881 

.2677 

514 

44 

16 

293 

752 

.2232 

421 

44 

17 

955 

928 

.2670 

496 

43 

17 

316 

800 

.2225 

402 

43 

18 

.61978 

.78975 

.2662 

478 

42 

18 

338 

849 

.2218 

384 

42 

19 

.62001 

.79022 

.2655 

460 

41 

19 

361 

898 

.2210 

366 

41 

20 

.62024 

.79070 

1.2647 

.78442 

40 

20 

.63383 

.81946 

1.2203 

.77347 

40 

21 

046 

117 

.2640 

424 

39 

21 

406 

.81995 

.2196 

329 

39 

22 

069 

164 

.2632 

405 

38 

22 

428 

.82044 

.2189 

310 

38 

23 

092 

212 

.2624 

387 

37 

23 

451 

092 

.2181 

292 

37 

24 

115 

259 

.2617 

369 

36 

24 

473 

141 

.2174 

273 

36 

25 

.62138 

.79306 

1.2609 

.73351 

35 

25 

.63496 

.82190 

1.2167 

.77255 

35 

26 

160 

354 

.2602 

333 

34 

26 

518 

238 

.2160 

236 

34 

27 

183 

401 

.2594 

315 

33 

27 

540 

287 

.2153 

218 

33 

28 

206 

449 

.2587 

297 

32 

28 

563 

336 

.2145 

199 

32 

29 

229 

496 

.2579 

279 

31 

29 

585 

385 

.2138 

181 

31 

30 

.62251 

.79544 

1.2572 

.78261 

30 

30 

.63608 

.82434 

1.2131 

.77162 

30 

31 

274 

591 

.2564 

243 

29 

31 

630 

483 

.2124 

144 

29 

32 

297 

639 

.2557 

225 

28 

32 

653 

531 

.2117 

125 

28 

33 

320 

686 

.2549 

206 

27 

33 

675 

580 

.2109 

107 

27 

34 

342 

734 

.2542 

188 

26 

34 

698 

629 

.2102 

088 

26 

35 

.62365 

.79781 

1.2534 

.78170 

25 

35 

.63720 

.82678 

1.2095 

.77070 

25 

36 

-388 

829 

.2527 

152 

24 

36 

742 

727 

.2088 

051 

24 

37 

411 

877 

.2519 

134 

23 

37 

765 

776 

.2081 

033 

23 

38 

433 

924 

.2512 

116 

22 

38 

787 

825 

.2074 

.77014 

22 

39 

456 

.79972 

.2504 

098 

21 

39 

810 

874 

.2066 

.76996 

21 

40 

.62479 

.80020 

1.2497 

.78079 

20 

40 

.63832 

.82923 

1.2059 

.76977 

20 

41 

502 

067 

.2489 

061 

19 

41 

854 

.82972 

.2052 

959 

19 

42 

524 

115 

.2482 

043 

18 

42 

877 

.83022 

.2045 

940 

18 

43 

547 

163 

.2475 

025 

17 

43 

899 

071 

.2038 

921 

17 

44 

570 

211 

.2467 

.78007 

16 

44 

922 

120 

.2031 

903 

16 

45 

.62592 

.80258 

1.2460 

.77988 

15 

45 

.63944 

.83169 

1.2024 

.76884 

15 

46 

615 

306 

.2452 

970 

14 

46 

966 

218 

.2017 

866 

14 

47 

638 

354 

.2445 

952 

13 

47 

.63989 

268 

.2009 

847 

13 

48 

660 

402 

.2437 

934 

12 

48 

.64011 

317 

.2002 

828 

12 

49 

683 

450 

.2430 

916 

11 

49 

033 

366 

.1995 

810 

11 

50 

.62706 

.80498 

1.2423 

.77897 

10 

50 

.64056 

.83415 

1.1988 

.76791 

10 

51 

728 

546 

.2415 

879 

9 

51 

078 

465 

.1981 

772 

9 

52 

751 

594 

.2408 

861 

8 

52 

100 

514 

.1974 

754 

8 

53 

774 

642 

.2401 

843 

7 

53 

123 

564 

.1967 

735 

7 

54 

796 

690 

.2393 

824 

6 

54 

145 

613 

.1960 

717 

6 

55 

.62819 

.80738 

1.2386 

.77806 

5 

55 

.64167 

.83662 

1.1953 

.76698 

5 

56 

842 

786 

.2378 

788 

4 

56 

190 

712 

.1946 

679 

4 

57 

864 

834 

.2371 

769 

3 

57 

212 

761 

.1939 

661 

3 

58 

887 

882 

.2364 

751 

2 

58 

234 

811 

.1932 

642 

2 

59 

909 

930 

.2356 

733 

1 

59 

256 

860 

.1925 

623 

1 

60 

.62932 

.80978 

1.2349 

.77715 

0 

60 

.64279 

.83910 

1.1918 

.76604 

0 

Cos 

Ctn 

Tan 

Sin 

' 

Cos   Ctn 

Tan 

Sin 

' 

51C 


50C 


42 


40°  —  Values  of  Trigonometric  Functions  —  41C 


[II 


/ 

Sin 

Tan 

Ctn 

Cos 

1 

Sin 

Tan 

Ctn 

Cos 

0 

.64279 

.83910 

1.1918 

.76604 

60 

0 

.65606 

.86929 

1.1504 

.75471 

60 

1 

301 

.83960 

.1910 

586 

59 

1 

628 

.86980 

.1497 

452 

59 

2 

323 

.84009 

.1903 

567 

58 

2 

650 

.87031 

.1490 

433 

58 

3 

346 

059 

.1896 

548 

57 

3 

672 

082 

.1483 

414 

57 

4 

368 

108 

.1889 

530 

56 

4 

694 

133 

.1477 

395 

56 

5 

.64390 

.84158 

1.1882 

.76511 

55 

5 

.65716 

.87184 

1.1470 

.75375 

55 

6 

412 

208 

.1875 

492 

54 

6 

738 

236 

.1463 

356 

54 

7 

435 

258 

.1868 

473 

53 

7 

759 

287 

.1456 

337 

53 

8 

457 

307 

.1861 

455 

52 

8 

781 

338 

.1450 

318 

52 

9 

479 

357 

.1854 

436 

51 

9 

803 

389 

.1443 

299 

51 

10 

.64501 

.84407 

1.1847 

.76417 

50 

10 

.65825 

.87441 

1.1436 

.75280 

50 

11 

524 

457 

.1840 

398 

49 

11 

847 

492 

.1430 

261 

49 

12 

546 

507 

.1833 

380 

48 

12 

869 

543 

.1423 

241 

48 

13 

568 

556 

.1826 

361 

47 

13 

891 

595 

.1416 

222 

47 

14 

590 

606 

.1819 

342 

46 

14 

913 

646 

.1410 

203 

46 

15 

.64612 

.84656 

1.1812 

.76323 

45 

15 

.65935 

.87698 

1.1403 

.75184 

45 

16 

635 

706 

.1806 

304 

44 

16 

956 

749 

.1396 

165 

44 

17 

657 

756 

.1799 

286 

43 

17 

.65978 

801 

.1389 

146 

43 

18 

679 

806 

.1792 

267 

42 

18 

.66000 

852 

.1383 

126 

42 

19 

701 

856 

.1785 

248 

41 

19 

022 

904 

.1376 

107 

41 

20 

.64723 

.84906 

1.1778 

.76229 

40 

20 

.66044 

.87955 

1.1369 

.75088 

40 

21 

746 

.84956 

.1771 

210 

39 

21 

066 

.88007 

.1363 

069 

39 

22 

768 

.85006 

.1764 

192 

38 

22 

088 

059 

.1356 

050 

38 

23 

790 

057 

.1757 

173 

37 

23 

109 

110 

.1349 

030 

37 

24 

812 

107 

.1750 

154 

36 

24 

131 

162 

.1343 

.75011 

36 

25 

.64834 

.85157 

1.1743 

.76135 

35 

25 

.66153 

.88214 

1.1336 

.74992 

35 

26 

856 

207 

.1736 

116 

34 

26 

175 

265 

.1329 

973 

34 

27 

878 

257 

.1729 

097 

33 

27 

197 

317 

.1323 

953 

33 

28 

901 

308 

.1722 

078 

32 

28 

218 

369 

.1316 

934 

32 

29 

923 

358 

.1715 

059 

31 

29 

240 

421 

.1310 

915 

31 

30 

64945 

.85408 

1.1708 

.76041 

30 

30 

.66262 

.88473 

1.1303 

.74896 

30 

31 

967 

458 

.1702 

022 

29 

31 

284 

524 

.1296 

876 

29 

32 

.64989 

509 

.1695 

.76003 

28 

32 

306 

576 

.1290 

857 

28 

33 

.65011 

559 

.1688 

.75984 

27 

33 

327 

628 

.1283 

838 

27 

34 

033 

609 

.1681 

965 

26 

34 

349 

680 

.1276 

818 

26 

35 

.65055 

.85660 

1.1674 

.75946 

25 

35 

.66371 

.88732 

1.1270 

.74799 

25 

36 

077 

710 

.1667 

927 

24 

36 

393 

784 

.1263 

780 

24 

37 

100 

761 

.1660 

908 

23 

37 

414 

836 

.1257 

760 

23 

38 

122 

811 

.1653 

889 

22 

38 

436 

888 

.1250 

741 

22 

39 

144 

862 

.1647 

870 

21 

39 

458 

940 

.1243 

722 

21 

40 

.65166 

.85912 

1.1640 

.75851 

20 

40 

.66480 

.88992 

1.1237 

.74703 

20 

41 

188 

.85963 

.1633 

832 

19 

41 

501 

.89045 

.1230 

683 

19 

42 

210 

.86014 

.1626 

813 

18 

42 

523 

097 

.1224 

664 

18 

43 

232 

064 

.1619 

794 

17 

43 

545 

149 

.1217 

644 

17 

44 

254 

115 

.1612 

775 

16 

44 

566 

201 

.1211 

625 

16 

45 

.65276 

.86166 

1.1606 

.75756 

15 

45 

.66588 

.89253 

1.1204 

.74606 

15 

46 

298 

216 

.1599 

738 

14 

46 

610 

306 

.1197 

586 

14 

47 

320 

267 

.1592 

719 

13 

47 

632 

358 

.1191 

567 

13 

48 

342 

318 

.1585 

700 

12 

48 

653 

410 

.1184 

548 

12 

49 

364 

368 

.1578 

680 

11 

49 

675 

463 

.1178 

528 

11 

50 

.65386 

.86419 

1.1571 

.75661 

10 

50 

.66697 

.89515 

1.1171 

.74509 

10 

51 

408 

470 

.1565 

642 

9 

51 

718 

567 

.1165 

489 

9 

52 

430 

521 

.1558 

623 

8 

52 

740 

620 

.1158 

470 

8 

53 

452 

572 

.1551 

604 

7 

53 

762 

672 

.1152 

451 

7 

54 

474 

623 

.1544 

585 

6 

54 

783 

725 

.1145 

431 

6 

55 

.65496 

.86674 

1.1538 

.75566 

5 

55 

.66805 

.89777 

1.1139 

.74412 

5 

56 

518 

725 

.1531 

547 

4 

56 

827 

830 

.1132 

392 

4 

57 

540 

776 

.1524 

528 

3 

57 

848 

883 

.1126 

373 

3 

58 

562 

827 

.1517 

509 

2 

58 

870 

935 

.1119 

353 

2 

59 

584 

878 

.1510 

490 

1 

59 

891 

.89988 

.1113 

334 

1 

60 

.65606 

.86929 

1.1504 

.75471 

0 

60 

.66913 

.90040 

1.1106 

.74314 

0 

Cos 

Ctn 

Tan 

Sin 

1 

Cos 

Ctn 

Tan 

Sin 

/ 

49C 


48C 


II]         42°  —  Values  of  Trigonometric  Functions  —  43C 


43 


/ 

Sin 

Tan 

Ctn 

Cos 

' 

Sin 

Tan 

Ctn 

Cos 

0 

.66913 

.90040 

1.1106 

.74314 

60 

0 

.68200 

.93252 

1.0724 

.73135 

60 

1 

935 

093 

.1100 

295 

59 

1 

221 

306 

.0717 

116 

59 

2 

956 

146 

.1093 

276 

58 

2 

242 

360 

.0711 

096 

58 

3 

978 

199 

.1087 

256 

57 

3 

264 

415 

.0705 

076 

57 

4 

.66999 

251 

.1080 

237 

56 

4 

285 

469 

.0699 

056 

56 

5 

.67021 

.90304 

1.1074 

.74217 

55 

5 

.68306 

.93524 

1.0692 

.73036 

55 

6 

043 

357 

.1067 

198 

54 

6 

327 

578 

.0686 

.73016 

54 

7 

064 

410 

.1061 

178 

53 

7 

349 

633 

.0680 

.72996 

53 

8 

086 

463 

.1054 

159 

52 

8 

370 

688 

.0674 

976 

52 

9 

107 

516 

.1048 

139 

51 

9 

391 

742 

.0668 

957 

51 

10 

.67129 

.90569 

1.1041 

.74120 

50 

10 

.68412 

.93797 

1.0661 

.72937 

50 

11 

151 

621 

.1035 

100 

49 

11 

434 

oC^ 

.0655 

917 

49 

12 

172 

674 

.1028 

080 

48 

12 

455 

906 

.0649 

897 

48 

13 

194 

727 

.1022 

061 

47 

13 

476 

.93901 

.0643 

877 

47 

14 

215 

781 

.1016 

041 

46 

14 

497 

.94016 

.0637 

857 

46 

15 

.67237 

.90834 

1.1009 

.74022 

45 

15 

.68518 

.94071 

1.0630 

.72837 

45 

16 

258 

887 

.1003 

.74002 

44 

16 

539 

125 

.0624 

817 

44 

17 

280 

940 

.0996 

.73983 

43 

17 

561 

180 

.0618 

797 

43 

18 

301 

.90993 

.0990 

963 

42 

18 

582 

235 

.0612 

777 

42 

19 

323 

.91046 

.0983 

944 

41 

19 

603 

290 

.0606 

757 

41 

20 

.67344 

.91099 

1.0977 

.73924 

40 

20 

.68624 

.94345 

1.0599 

.72737 

40 

21 

366 

153 

.0971 

904 

39 

21 

645 

400 

.0593 

717 

39 

22 

387 

206 

.0964 

885 

38 

22 

666 

455 

.0587 

697 

38 

23 

409 

259 

.0958 

865 

37 

23 

688 

510 

.0581 

677 

37 

24 

430 

313 

.0951 

846 

36 

24 

709 

565 

.0575 

657 

36 

25 

.67452 

.91366 

1.0945 

.73826 

35 

25 

.68730 

.94620 

1.0569 

.72637 

35 

26 

473 

419 

.0939 

806 

34 

26 

751 

676 

.0562 

617 

34 

27 

495 

473 

.0932 

787 

33 

27 

772 

731 

.0556 

597 

33 

28 

516 

526 

.0926 

767 

32 

28 

793 

786 

.0550 

577 

32 

29 

538 

580 

.0919 

747 

31 

29 

814 

841 

.0544 

557 

31 

30 

.67559 

.91633 

1.0913 

.73728 

30 

30 

.68835 

.94896 

1.0538 

.72537 

30 

31 

580 

687 

.0907 

708 

29 

31 

857 

.94952 

.0532 

517 

29 

32 

602 

740 

.0900 

688 

28 

32 

878 

.95007 

.0526 

497 

28 

33 

623 

794 

.0894 

669 

27 

33 

899 

062 

.0519 

477 

27 

34 

645 

847 

.0888 

649 

26 

34 

920 

118 

.0513 

457 

26 

35 

.67666 

.91901 

1.0881 

.73629 

25 

35 

.68941 

.95173 

1.0507 

.72437 

25 

36 

688 

.91955 

.0875 

610 

24 

36 

962 

229 

.0501 

417 

24 

37 

709 

.92008 

.0869 

590 

23 

37 

.68983 

284 

.0495 

397 

23 

38 

730 

062 

.0862 

570 

22 

38 

.69004 

340 

.0489 

377 

22 

39 

752 

116 

.0856 

551 

21 

39 

025 

395 

.0483 

357 

21 

40 

.67773 

.92170 

1.0850 

.73531 

20 

40 

.69046 

.95451 

1.0477 

.72337 

20 

41 

795 

224 

.0843 

511 

19 

41 

067 

506 

.0470 

317 

19 

42 

816 

277 

.0837 

491 

18 

42 

088 

562 

.0464 

297 

18 

43 

837 

331 

.0831 

472 

17 

43 

109 

618 

.0458 

277 

17 

44 

859 

385 

.0824 

452 

16 

44 

130 

673 

-0452 

257 

16 

45 

.67880 

.92439 

1.0818 

.73432 

15 

45 

.69151 

.95729 

1.0446 

.72236 

15 

46 

901 

493 

.0812 

4J£ 

J4 

46 

172 

785 

.0440 

216 

14 

47 

923 

547 

.0805 

393 

13 

47 

193 

841 

.0434 

196 

13 

48 

944 

601 

.0799 

37? 

12 

48 

214 

897 

.0428 

176 

12 

49 

965 

655 

.0793 

353 

11 

49 

235 

.95952 

.0422 

156 

11 

50 

.67987 

.92709 

1.0786 

.73333 

10 

50 

.69256 

.96008 

1.0416 

.72136 

10 

51 

.68008 

763 

.0780 

314 

9 

51 

277 

064 

.0410 

116 

9 

52 

029 

817 

.0774 

294 

8 

52 

298 

120 

.0404 

095 

8 

53 

051 

872 

.0768 

274 

7 

53 

319 

176 

.0398 

075 

7 

54 

072 

926 

.0761 

254 

6 

54 

340 

232 

.0392 

055 

6 

55 

.68093 

.92980 

1.0755 

.73234 

5 

55 

.69361 

.96288 

1.0385 

.72035 

5 

56 

115 

.93034 

.0749 

215 

4 

56 

382 

344 

.0379 

.72015 

4 

57 

136 

088 

.0742 

195 

3 

57 

403 

400 

.0373 

.71995 

3 

58 

157 

143 

.0736 

175 

2 

58 

424 

457 

.0367 

974 

2 

59 

179 

197 

.0730 

155 

1 

59 

445 

513 

.0361 

954 

1 

60 

.68200 

.93252 

1.0724 

.73135 

0 

60 

.69466 

.96569 

1.0355 

.71934 

0 

Cos 

Ctn 

Tan 

Sin 

/ 

Cos 

Ctn 

Tan 

Sin 

/ 

47C 


46C 


44 


44°  —  Values  of  Trigonometric  Functions 


1 

Sin 

Tan 

Ctn 

Cos 

0 

.69466 

.96569 

1.0355 

.71934 

60 

1 

487 

625 

.0349 

914 

59 

2 

508 

681 

.0343 

894 

58 

3 

529 

738 

.0337 

873 

57 

4 

549 

794 

.0331 

853 

56 

5 

.69570 

.96850 

1.0325 

.71833 

55 

6 

591 

907 

.0319 

813 

54 

7 

612 

.96963 

.0313 

792 

53 

8 

633 

.97020 

.0307 

111 

52 

9 

654 

076 

.0301 

752 

51 

10 

.69675 

.97133 

1.0295 

.71732 

50 

11 

696 

189 

.0289 

711 

49 

12 

717 

246 

.0283 

691 

48 

13 

737 

302 

.0277 

671 

47 

14 

758 

359 

.0271 

650 

46 

15 

.69779 

.97416 

1.0265 

.71630 

45 

16 

800 

472 

.0259 

610 

44 

17 

821 

529 

.0253 

590 

43 

18 

842 

586 

.0247 

569 

42 

19 

862 

643 

.0241 

549 

41 

20 

.69883 

.97700 

1.0235 

.71529 

40 

21 

904 

756 

.0230 

508 

39 

22 

925 

813 

.0224 

488 

38 

23 

946 

870 

.0218 

468 

37 

24 

966 

927 

.0212 

447 

36 

25 

.69987 

.97984 

1.0206 

.71427 

35 

26 

.70008 

.98041 

.0200 

407 

34 

27 

029 

098 

.0194 

386 

33 

28 

049 

155 

.0188 

366 

32 

29 

070 

213 

.0182 

345 

31 

30 

.70091 

.98270 

1.0176 

.71325 

30 

31 

112 

327 

.0170 

305 

29 

32 

132 

384 

.0164 

284 

28 

33 

153 

441 

.0158 

264 

27 

34 

174 

499 

.0152 

243 

26 

35 

.70195 

.98556 

1.0147 

.71223 

25 

36 

215 

613 

.0141 

203 

24 

37 

236 

671 

.0135 

182 

23 

38 

257 

728 

.0129 

162 

22 

39 

277 

786 

.0123 

141 

21 

40 

.70298 

.98843 

1.0117 

.71121 

20 

41 

319 

901 

.0111 

100 

19 

42 

339 

.98958 

.0105 

080 

18 

43 

360 

.99016 

.0099 

059 

17 

44 

381 

073 

.0094 

039 

16 

45 

.70401 

.99131 

1.0088 

.71019 

15 

46 

422 

189 

.0082 

.70998 

14 

47 

443 

247 

.0076 

978 

13 

48 

463 

304 

.0070 

957 

12 

49 

484 

362 

.0064 

937 

11 

50 

.70505 

.99420 

1.0058 

.70916 

10 

51 

525 

478 

.0052 

896 

0 

52 

546 

536 

.0047 

875 

8 

53 

567 

594 

.0041 

855 

7 

54 

587 

652 

.0035 

834 

6 

55 

.70608 

.99710 

1.0029 

.70813 

5 

56 

628 

768 

.0023 

793 

4 

57 

649 

826 

.0017 

772 

3 

58 

670 

884 

.0012 

752 

2 

59 

690 

.99942 

.0006 

731 

1 

60 

.70711 

1.0000 

1.0000 

.70711 

0 

Cos 

Ctn 

Tan 

Sin 

/ 

45C 


TABLE  IH 


COMMON  LOGARITHMS 

OF  THE 

TRIGONOMETRIC  FUNCTIONS 

FROM 

0°  TO  90°  AT  INTERVALS  OF  ONE  MINUTE 

TO 

FIVE  DECIMAL  PLACES 

From  each  logarithm  given,  subtract  10 


Table  Ilia— Auxiliary  Table  of  S  and  T  for  A  in  Minutes 

S  =  log  sin  A  —  log  A'     and     T  =  log  tan  A  —  log  A' 


A' 

S+10 

0'  - 

13' 

6.46373 

14'  - 

42' 

72 

43'  - 

58' 

71 

59'  - 

71' 

6.46370 

72'  - 

81' 

69 

82'  - 

91' 

68 

92'  - 

99' 

6.46367 

100'  - 

107' 

66 

108'  - 

115' 

65 

116'  - 

121' 

6.46364 

122'  — 

128' 

63 

129'  - 

134' 

62 

135'  - 

140' 

6.46361 

141'  - 

146' 

60 

147'  - 

151' 

59 

152'  - 

157' 

6.46358 

158'  - 

162' 

57 

163'  - 

167' 

56 

168'  - 

171' 

6.46355 

172'  - 

176' 

54 

177'  - 

181' 

53 

A1 

r+io 

0'  - 

26' 

6.46373 

27'  - 

39' 

74 

40'  - 

48' 

75 

49'  - 

56' 

6.46376 

57'  - 

63' 

77 

64'  - 

69' 

78 

70'  - 

74' 

6.46379 

75'  - 

80' 

80 

81'  - 

85' 

81 

86'  - 

89' 

6.46382 

90'  - 

94' 

83 

95'  - 

98' 

84 

99'  - 

102' 

6.46385 

103'  - 

106' 

86 

107'  - 

110' 

87 

111'  - 

113' 

6.46388 

114'  - 

117' 

89 

118'  - 

120' 

90 

121'  - 

124' 

6.46391 

125'  - 

127' 

92 

128'  - 

130' 

93 

A' 

T+10 

131'  - 

133' 

6.46394 

134'  - 

136' 

95 

137'  - 

139' 

96 

140'  - 

142' 

6.46397 

143'  - 

145' 

98 

146'  - 

148' 

99 

149'  - 

150' 

6.46400 

151'  - 

153' 

01 

154'  - 

156' 

02 

157'  - 

158' 

6.46403 

159'  - 

161' 

04 

162'  - 

163' 

05 

164'  - 

166' 

6.46406 

167'  - 

168' 

07 

169'  - 

171' 

08 

172'  - 

173' 

6.46409 

174'  - 

175' 

10 

176'  - 

178' 

11 

179'  - 

180' 

6.46412 

181'  - 

182' 

13 

183'  - 

184' 

14 

For  small  angles:     log  sin  A  =  log  A'  +  S     and     log  tan  A  =  log  A'  +  T. 
For  angles  near  90°:  log  cos  A  =  log  (90°  -  A)'  +  S,  log  ctn  A  =  log  (90°  -  A)' 
+  T  where  A'  =  number  of  minutes  in  A,  and  (90°  —  A)'  =  number  of  minutes 
in  90°  -  A. 

45 


46 


0°  —  Logarithms  of  Trigonometric  Functions 


' 

LSin 

d 

LTan 

cd 

LCtn 

L  Cos 

in  on  nnn 

fin 

1 

6.46  373 

6.46  373 

13.53  627 

AV.Ul/  v/UU 

10.00  000 

DU 

59 

2 

6.76  476 

30103 

6.76  476 

30103 

13.23  524 

10.00  000 

58 

3 

6.94  085 

17609 

6.94  085 

17609 

13.05  915 

10.00  000 

57 

4 

7.06  579 

12494 

7.06  579 

12494 

12.93  421 

10.00  000 

56 

5 

7.16  270 

9691 

7.16270 

9691 

12.83  730 

10.00  000 

55 

6 

7.24  188 

7918 

7.24  188 

7918 

12.75  812 

10.00  000 

54 

7 

7.30  882 

6694 

7.30  882 

6694 

12.69  118 

10.00  000 

53 

8 

7.36  682 

5800 

7.36  682 

5800 

12.63  318 

10.00  000 

52 

9 

7.41  797 

5115 

7.41  797 

5115 

12.58  203 

10.00  000 

51 

o      ||| 

10 

7.46  373 

7.46  373 

12.53  627 

10.00  000 

50 

11 

7.50  512 

4139 

7.50512 

4139 

12.49  488 

10.00  000 

49 

S                bD  3 

12 

7.54  291 

3779 

7.54  291 

3779 

12.45  709 

10.00  000 

48 

^    .  .•  fl  .2 

13 

7.57  767 

3476 

7.57  767 

3476 

12.42  233 

10.00  000 

47 

'C  52  ^  J*  f^ 

14 

7.60  985 

3218 

7.60  986 

3219 

12.39  014 

10.00  000 

46 

-fr3    fe    O 

15 

7.63  982 

2997 

7.63  982 

2996 

12.36  018 

10.00  000 

45 

°  ^^  •**  '"§ 

16 

7.66  784 

2802 

7.66  785 

2803 

12.33  215 

10.00  000 

44 

t-  cf  >•>  ^  "3 

17 

7.69  417 

2633 

7.69  418 

2633 

12.30  582 

9.99  999 

43 

O   *—  1   £3   "H     £^ 

18 

7.71  900 

2483 

7.71  900 

2482 

12.28  100 

9.99  999 

42 

^"'K    3  Jfi    o3 

19 

7.74  248 

2348 

7.74  248 

2348 

12.25  752 

9.99  999 

41 

co  o>  M  3  "t5 

20 

7.76  475 

2227 

7.76  476 

2228 

12.23  524 

9.99  999 

40 

e)  3  ^  w  — 

21 

7.78  594 

2119 

7.78  595 

2119 

12.21  405 

9.99  999 

39 

r-j  C-i  ''"',     t->     O 

22 

7.80  615 

2021 

7.80  615 

2020 

12.19385 

9.99  999 

38 

23 

7.82  545 

1930 

7.82  546 

1931 

12.17  454 

9.99  999 

37 

W     §^  j3     (D     O 

24 

7.84  393 

1848 

7.84  394 

1848 

12.15  606 

9.99  999 

36 

V    w   ~S  3  -5 

25 

7.86  166 

1773 

7.86  167 

1773 

12.13  833 

9.99  999 

35 

1—1  ^   fl   -3     ® 

26 

7.87  870 

1704 

7.87  871 

1704 

12.12  129 

9.99  999 

34 

£  ?-.  +3    03    « 

27 

7.89  509 

1639 

7.89  510 

1639 

12.10490 

9.99  999 

33 

5P03    2  IS     ^ 

28 

7.91  088 

1579 

7.91  089 

1579 

12.08911 

9.99  999 

32 

M     r*  f^     •  •*     tn 

o3    5  -^          o3 

29 

7.92  612 

1524 

7.92  613 

1524 

12.07  387 

9.99  998 

31 

*      -.  3    c 

30 

7.94  084 

1472 

7.94  086 

1473 

12.05  914 

9.99  998 

30 

o  -^>  6*    •9 

^,0         f  t 

31 

7.95  508 

1424 

7.95  510 

1424 

12.04  490 

9.99  998 

29 

-*j>    Q)    o3  CN    Q 

32 

7.96  887 

1379 

7.96  889 

1379 

12.03  111 

9.99  998 

28 

§  ~c3  "o  "^    ° 

33 

7.98  223 

1336 

7.98  225 

1336 

12.01  775 

9.99  998 

27 

bC  O>    £<    2  t^ 

34 

7.99  620 

1297 

7.99  522 

1297 

12.00  478 

9.99  998 

26 

2    Sb    „         14- 

35 

8.00  779 

1259 

8.00  781 

1259 

11.99219 

9.99  998 

25 

^  O      .1^ 

36 

8.02  002 

1223 

8.02  004 

1223 

11.97996 

9.99  998 

24 

o  "Eb  ^  ^  ^ 

37 

8.03  192 

1190 

8.03  194 

1190 

11.96806 

9.99  997 

23 

M      0      t-t    *t-t      gj 

38 

8.04  350 

1158 

8.04  353 

1159 

11.95  647 

9.99  997 

22 

39 

8.05  478 

1128 

8.05  481 

1128 

11.94519 

9.99  997 

21 

•9  *g  3    <U  T3 

40 

8.06  578 

1100 

8.06  581 

1100 

11.93419 

9.99  997 

20 

^    w  "^  "08  .2 

41 

8.07  650 

1072 

8.07  653 

1072 

11.92347 

9.99  997 

19 

O  -g    o3  "w  *3 

42 

8.08  696 

1046 

8.08  700 

1047 

11.91300 

9.99  997 

18 

W    §  'B    co    ^ 

43 

8.09  718 

1022 

8.09  722 

1022 

11.90278 

9.99  997 

17 

S  kp^  ~£  *-" 

44 

8.10717 

999 

8.10  720 

998 

11.89  280 

9.99  996 

16 

^  §  •+*  a,  "o 

45 

8.11  693 

976 

8.11  696 

976 

11.88304 

9.99  996 

15 

'*•-       "O        2    —  •        C 

46 

8.12  647 

954 

8.12651 

955 

11.87349 

9.99  996 

14 

wi  °  •*»  rt  .2 

47 

8.13  581 

934 

8.13  585 

934 

11.86415 

9.99  996 

13 

-2  o  a  §  s» 

48 

8.14  495 

914 

8.14  500 

915 

11.85  500 

9.99  996 

12 

~  S  S  '-P  » 

49 

8.15391 

896 

8.15  395 

895 

11.84605 

9.99  996 

11 

°    v  L»    O    2 

50 

8.16  268 

877 

8.16  273 

878 

11.83727 

9.99  995 

10 

"to          O    o 

51 

8.17  128 

860 

8.17  133 

860 

11.82867 

9.99  995 

9 

O         I*    w 

52 

8.17971 

843 

8.17  976 

843 

11.82024 

9.99  995 

8 

O          ft  eJ 

53 

8.18798 

827 

8.18  804 

828 

11.81  196 

9.99  995 

7 

54 

8.19610 

812 

8.19  616 

812 

11.80384 

9.99  995 

6 

55 

8.20  407 

797 

8.20413 

797 

11.79  587 

9.99  994 

5 

56 

8.21  189 

782 

8.21  195 

782 

11.78805 

9.99  994 

4 

57 

8.21  958 

769 

8.21  964 

769 

11.78036 

9.99  994 

3 

58 

8.22713 

755 

8.22  720 

756 

11.77280 

9.99  994 

2 

59 

8.23  456 

743 

8.23  462 

742 

11.76538 

9.99  994 

1 

60 

8.24  186 

730 

8.24  192 

730 

11.75808 

9.99  993 

0 

LCos 

d 

L  Ctn 

cd 

L  Tan 

LSin 

' 

89°  —  Logarithms  of  Trigonometric  Functions 


Ill]          1°  —  Logarithms  of  Trigonometric  Functions 


47 


1 

LSin 

d 

LTan 

cd 

LCtn 

L  Cos 

Prop.  Pts. 

0 

8.24  186 

8.24  192 

11.75808 

9.99  993 

60 

1 

8.24  903 

717 

8.24  910 

718 

11.75090 

9.99  993 

59 

710     690     670     650 

2 
3 

8.25  609 
8.26  304 

706 
695 

8.25  616 
8.26312 

706 
696 

11.74384 
11.73  688 

9.99  993 
9.99  993 

58 
57 

2 

3 
4 

142     138     134     130 
213     207     201     195 
284     276     268     260 

4 

8.26  988 

684 

8.26  996 

684 

11.73004 

9.99  992 

56 

5 

355     345     335     325 

673 

673 

6 

426     414     402     390 

5 

8.27  661 

8.27  669 

11.72  331 

9.99  992 

55 

7 

497     483     469     455 

6 

7 

8.28  324 
8.28  977 

663 
653 

8.28  332 
8.28  986 

663 
654 

11.71  668 
11.71  014 

9.99  992 
9.99  992 

54 
53 

8 
9 

568     552     536     520 
639     621     603     585 

8 

8.29  621 

644 

8.29  629 

643 

11.70371 

9.99  992 

52 

eso    690    6io     finn 

9 

8.30  255 

634 
624 

8.30  263 

634 
625 

11.69  737 

9.99  991 

51 

2 

126     124     122     120 

10 

8.30  879 

8.30  888 

11.69  112 

9.99  991 

50 

3 

189     186     183     180 

11 

8.31  495 

616 

8.31  505 

617 

11.68495 

9.99  991 

49 

4 
5 

252     248     244     240 
315     310     305     300 

12 

8.32  103 

oOs 

8.32  112 

607 

11.67  888 

9.99  990 

48 

6 

378     372     366     360 

13 

8.32  702 

599 

8.32711 

599 

11.67289 

9.99  990 

47 

7 
3 

441     434     427     420 
504     496     488     480 

14 

8.33  292 

590 
583 

8.33  302 

591 
584 

11.66698 

9.99  990 

46 

9 

567     558     549     540 

15 

8.33  875 

8.33  886 

11.66  114 

9.99  990 

45 

16 

8.34  450 

575 

8.34  461 

575 

11.65539 

9.99  989 

44 

590     580     570     560 

17 
18 

8.35  018 
8.35  578 

568 
560 

8.35  029 
8.35  590 

568 
561 

11.64971 
11.64410 

9.99  989 
9.99  989 

43 

42 

2 

3 
4 

118     116     114     112 
177     174     171     168 
236     232     228     224 

19 

8.36  131 

553 

8.36  143 

553 

11.63  857 

9.99  989 

41 

5 

295     290     285     280 

547 

546 

6 

354     348     342     336 

20 

8.36  678 

8.36  689 

11.63311 

9.99  988 

40 

7 

413     406     399     392 

21 
22 

8.37217 
8.37  750 

539 
533 

8.37  229 
8.37  762 

540 
533 

11.62771 
11.62238 

9.99  988 
9.99  988 

39 
38 

8 
9 

472     464     456     448 
531     522     513     504 

23 

8.38  276 

526 

8.38  289 

527 

11.61711 

9.99  987 

37 

ssn     B40     san     BSO 

24 

8.38  796 

520 
514 

8.38  809 

520 

514 

11.61  191 

9.99  987 

36 

2 

110     108     106     104 

25 

8.39  310 

8.39  323 

11.60677 

9.99  987 

35 

3 

165     162     159     156 

26 

8.39  818 

508 

8.39  832 

509 

11.60  168 

9.99  986 

34 

4 
5 

220     216     212     208 
275     270     265     260 

27 

8.40  320 

502 

8.40  334 

502 

11.59  666 

9.99  986 

33 

6 

330     324     318     312 

28 
29 

8.40  816 
8.41  307 

496 
491 
485 

8.40  830 
8.41  321 

496 
491 
486 

11.59  170 
11.58679 

9.99  986 
9.99  985 

32 
31 

7 
8 
9 

385     378     371     364 
440     432     424     416 
495     486     477     468 

30 

8.41  792 

8.41  807 

11.58  193 

9.99  985 

30 

31 

8.42  272 

480 

8.42  287 

480 

11.57713 

9.99  985 

29 

610     500     490     480 

32 

33 

8.42  746 
8.43  216 

474 
470 

8.42  762 
8.43  232 

475 
470 

11.57238 
11.56768 

9.99  984 
9.99  984 

28 
27 

2 

3 
4 

102     100       98       96 
153     150     147     144 
204     200     196     192 

34 

8.43  680 

464 

8.43  696 

464 

11.56304 

9.99  984 

26 

5 

255     250     245     240 

459 

460 

6 

306     300     294     288 

35 

8.44  139 

8.44  156 

11.55844 

9.99  983 

25 

7 

357     350     343     336 

36 
37 

8.44  594 
8.45  044 

455 
450 

8.44611 
8.45  061 

455 
450 

11.55  389 
11.54939 

9.99  983 
9.99  983 

24 
23 

8 
9 

408     400     392     384 
459     450    441     432 

38 

8.45  489 

445 

8.45  507 

446 

11.54493 

9.99  982 

22 

470      460      4SO      440 

39 

8.45  930 

441 
436 

8.45  948 

441 
437 

11.54052 

9.99  982 

21 

2 

94       92       90       88 

40 

8.46  366 

8.46  385 

11.53  615 

9.99  982 

20 

141     138     135     132 

41 

8.46  799 

433 

8.46  817 

432 

11.53  183 

9.99  981 

19 

4 

188     184     1*0     17S 
23b     23U     225     220 

42 

8.47  226 

427 

8.47  245 

428 

11.52  755 

9.99  981 

18 

6 

282     276     270     264 

43 

8.47  650 

424 

8.47  669 

424 
A  or* 

11.52331 

9.99  981 

17 

I 

329     322     315     308 
376     368     360     352 

44 

8.48  069 

419 

8.48  089 

4/U 

11.51911 

9.99  980 

16 

9 

423     414     405     396 

45 

8.48  485 

416 

8.48  505 

416 

11.51  495 

9.99  980 

15 

46 

8.48  896 

411 

8.48917 

412 

11.51  083 

9.99  979 

14 

430     420     410     400 

47 

8.49  304 

408 

8.49  325 

408 

Af\  1 

11.50675 

9.99  979 

13 

2 

3 

86       84       82       80 
129     126     123     120 

48 

8.49  708 

404 

8.49  729 

4U-1 

11.50271 

9.99  979 

12 

4 

172     168     164     160 

49 

8.50  108 

400 

8.50  130 

401 
397 

11.49  870 

9.99  978 

11 

5 

215     210     205     200 
258     252     246     240 

50 

8.50  504 

8.50  527 

11.49473 

9.99  978 

10 

7 

301     294     287     280 

51 
52 

8.50  897 
8.51  287 

393 
390 

8.50  920 
8.51310 

393 
390 

11.49  080 
11.48  690 

9.99  977 
9.99  977 

9 

8 

8 
9 

344     336     328     320 
387     378     369     360 

53 

8.51  673 

386 

8.51  696 

386 

11.48304 

9.99  977 

7 

390      380      370      360 

54 

8.52  055 

382 

Q7Q 

8.52  079 

383 

11.47  921 

9.99  976 

6 

2 

78       76       74       72 

55 

56 

8.52  434 
8.52  810 

Of  £7 

376 

8.52  459 
8.52  835 

376 

11.47  541 
11.47  165 

9.99  976 
9.99  975 

5 

4 

3 
4 
5 

117     114     111     108 
156     152     148     144 
195     190     185     180 

57 

8.53  183 

373 

8.53  208 

373 

11.46792 

9.99  975 

3 

6 

234     228     222     216 

58 

8.53  552 

369 

8.53  578 

370 

11.46422 

9.99  974 

2 

8 

273     266     259     252 
312     304     296     288 

59 

8.53  919 

367 
363 

8.53  945 

367 
363 

11.46055 

9.99  974 

1 

9 

351     342     333     324 

60 

8.54  282 

8.54  308 

11.45692 

9.99  974 

0 

L  Cus 

d 

LCtn 

cd 

L  Tan 

LSin 

' 

Prop.  Pts. 

88°  —  Logarithms  of  Trigonometric  Functions 


48 


2°  —  Logarithms  of  Trigonometric  Functions 


[HI 


' 

LSin 

d 

LTan 

cd 

L  Ctn 

L  Cos 

Prop.  Pts. 

0 

8.54  282 

8.54  308 

11.45692 

9.99  974 

60 

1 

8.54  642 

360 

8.54  669 

361 

11.45331 

9.99  973 

59 

360           355        350 

2 
3 

8.54  999 
8.55  354 

357 
355 

8.55  027 
8.55  382 

358 
355 

11.44973 
11.44  618 

9.99  973 
9.99  972 

58 
57 

2 

3 
4 

72           71.0       70 
108         106.5     105 
144         142.0     140 

4 

8.55  705 

351 

8.55  734 

352 

11.44266 

9.99  972 

56 

5 

180        177.5     175 

349 

349 

6 

216        213  0     210 

5 

8.56  054 

8.56  083 

11.43  917 

9.99  971 

55 

7 

252        248.5     245 

6 

8.56  400 

346 

8.56  429 

346 

11.43571 

9.99  971 

54 

8 

288        284.0     280 

7 

8.56  743 

343 

8.56  773 

344 

11.43  227 

9.99  970 

53 

9 

324        319.5     315 

8 

8.57  084 

341 

8.57  114 

341 

11.42886 

9.99  970 

52 

a4fi          44*1               QOR 

9 

8.57  421 

337 
336 

8.57  452 

338 
336 

11.42548 

9.99  969 

51 

2 

69.0       68           67.0 

10 

8.57  757 

8.57  788 

11.42  212 

9.99  969 

50 

3 

103.5     102         100.5 

11 

8.58  089 

332 

8.58  121 

333 

11.41879 

9.99  968 

49 

4 
5 

138.0     136         134.0 
172.5     170         167.5 

12 

8.58419 

330 

8.58451 

330 

11.41  549 

9.99  968 

48 

6 

207.0     204        201.0 

13 
14 

8.58  747 
8.59  072 

328 
325 
323 

8.58  779 
8.59  105 

328 
326 
323 

11.41221 
11.40895 

9.99  967 
9.99  967 

47 
46 

7 
8 
9 

241.5     238        234.5 
276.0     272        268.0 
310.5     306        301.5 

15 

8.59  395 

8.59  428 

11.40572 

9.99  967 

45 

16 

8.59  715 

320 

8.59  749 

321 

11.40251 

9.99  966 

44 

330          325       320 

17 

8.60  033 

318 

8.60  068 

319 

11.39932 

9.99  966 

43 

2 

66          65.0       64 

18 

8.60  349 

316 

O1  Q 

8.60  384 

316 

11.39616 

9.99  965 

42 

4 

99          97.5       96 
132         130.0     128 

19 

8.60  662 

olo 

01  1 

8.60  698 

314 

11.39  302 

9.99  964 

41 

5 

165         162.5     160 

20 

8.60  973 

oil 

8.61  009 

11.38991 

9.99  964 

40 

7 

198        195.0      192 
231        227.5     224 

21 

8.61  282 

309 

8.61319 

310 

11.38681 

9.99  963 

39 

8 

264         260.0      256 

22 

8.61  589 

307 

8.61  626 

307 

11.38374 

9.99  963 

38 

9 

297        292.5     283 

23 

8.61  894 

305 

8.61  931 

305 

11.38069 

9.99  962 

37 

am       am          ans 

24 

8.62  196 

302 
301 

8.62  234 

303 
301 

11.37766 

9.99  962 

36 

2 

63.0       62           61.0 

25 

8.62  497 

8.62  535 

11.37  465 

9.99  961 

35 

3 

94.5       93           9.  .5 

26 

8.62  795 

298 

8.62  834 

299 

11.37  166 

9.99  961 

34 

4 
5 

126.0     124         122.0 
157.5     155         152.5 

27 

8.63  091 

J9o 

8.63  131 

297 

11.36869 

9.99  960 

33 

6 

189.0     186         183.0 

28 
29 

8.63  385 
8.63  678 

294 
293 
290 

8.63  426 
8.63  718 

295 

292 
291 

11.36574 
11.36282 

9.99  960 
9.99  959 

32 
31 

7 
8 
9 

220.5     217         213.5 
252.0     248        244.0 
283.5     279         274.5 

30 

8.63  968 

8.64  009 

11.35991 

9.99  959 

30 

31 

8.64  256 

288 

8.64  298 

289 

11.35702 

9.99  958 

29 

300           296       290 

32 

8.64  543 

287 

8.64  585 

287 

11.35415 

9.99  958 

28 

2 

60          59.0       58 

33 

8.64  827 

284 

8.64  870 

285 

11.35  130 

9.99  957 

27 

3 

4 

90          88.5       87 
120         118.0     116 

34 

8.65  110 

283 

8.65  154 

284 

11.34846 

9.99  956 

26 

5 

150         147.5      145 

281 

281 

6 

180        1770     174 

35 

8.65  391 

8.65  435 

11.34565 

9.99  956 

25 

7 

210        206.5     203 

36 

8.65  670 

279 

8.65715 

280 

11.34285 

9.99  955 

24 

8 

240        236.0     232 

37 

8.65  947 

277 

8.65  993 

278 

11.34007 

9.99  955 

23 

9 

270        265.5     261 

38 

8.66  223 

276 

8.66  269 

276 

11.33731 

9.99  954 

22 

2SS         280             27S 

39 

8.66  497 

272 

8.66  543 

274 

11.33457 

9.99  954 

21 

2 

57.0       56           55.0 

40 

8.66  769 

8.66816 

11.33  184 

9.99  953 

20 

3 

85.5       84           82.5 

41 

8.67  039 

270 

8.67  087 

271 

11.32913 

9.99  952 

19 

4 
5 

114.0     112         110.0 
142.5     140         137.5 

42 

8.67  308 

zoy 

8.67  356 

269 

11.32644 

9.99  952 

18 

6 

171.0     108         165.0 

43 
44 

8.67  575 
8.67  841 

267 
266 

8.67  624 
8.67  890 

268 
266 

11.32376 
11.32  110 

9.99  951 
9.99  951 

17 
16 

7 
8 
9 

199.5     196         192.5 
228.C     224         220.0 
256.5     252         247.5 

45 

8.68  104 

263 

8.68  154 

264 

11.31846 

9.99  950 

15 

46 

8.68  367 

263 

8.68417 

263 

11.31583 

9.99  949 

14 

270           265        260 

47 

8.68  627 

260 

8.68  678 

261 

11.31322 

9.99  949 

13 

2 

3 

54          53.0       52 
81          79  5       78 

48 

8.68  886 

259 

8.68  938 

260 

11.31062 

9.99  948 

12 

4 

108        106.'0     104 

49 

8.69  144 

258 

8.69  196 

258 

11.30804 

9.99  948 

11 

5 

135         132.5      130 

256 

257 

6 

162         159.0      156 

50 

8.69  400 

8.69  453 

11.30547 

9.99  947 

10 

189         185.5     182 

51 
52 

8.69  654 
8.69  907 

254 
253 

8.69  708 
8.69  962 

255 
254 

11.30292 
11.30038 

9.99  946 
9.99  946 

9 

8 

8 
9 

216        212.0     208 
243        238.5     234 

53 

8.70  159 

252 

8.70214 

252 

oc  t 

11.29786 

9.99  945 

7 

255        250            245 

54 

8.70  409 

24Q 

8.70  465 

ZOl 

9J.Q 

11.29535 

9.99  944 

6 

2 

51.0       50          49.0 

55 

56 

8.70  658 
8.70  905 

247 

8.70  714 
8.70  962 

JIW 

248 

11.29286 
11.29038 

9.99  944 
9.99  943 

5 

4 

3 
5 

76.5       75           73.5 
102.0     100           98.0 
127.5     125         122.5 

57 

8.71  151 

246 

8.71  208 

246 

11.28792 

9.99  942 

3 

6 

153.0     150         147.0 

58 

8.71  395 

244 

8.71  453 

245 

11.28547 

9.99  942 

2 

7 
8 

178.5     175         171.5 
204  0     200         196  0 

59 

8.71  638 

242 

8.71  697 

244 
243 

11.28303 

9.99  941 

1 

9 

229.5     225        220.5 

60 

8.71  880 

8.71  940 

11.28060 

9.99  940 

0 

LCos 

d 

L  Ctn 

cd 

L  Tan 

LSin 

' 

Prop.  Pts. 

87°  —  Logarithms  of  Trigonometric  Functions 


Ill]          3°  —  Logarithms  of  Trigonometric  Functions 


49 


' 

LSin 

d 

LTan 

cd 

LCtn 

LCos 

Prop.  Pts. 

0 

8.71  880 

8.71  940 

11.28060 

9.99  940 

60 

1 

8.72  120 

240 

8.72  181 

241 

11.27819 

9.99  940 

59 

240          235       230 

2 

8.72  359 

239 

8.72  420 

239 

11.27  580 

9.99  939 

58 

2 

•3 

48          47.0       46 

•TO                »r/\   e           en 

3 

8.72  597 

238 

8.72  659 

239 

11.27341 

9.99  938 

57 

4 

•  &               /U.O          OV 

96          94.0       92 

4 

8.72  834 

237 

8.72  896 

237 

11.27  104 

9.99  938 

56 

5 

120        117.5     115 

235 

236 

(i 

144        141  0     138 

5 

8.73  069 

8.73  132 

11.26868 

9.99  937 

55 

7 

168        164'.5     161 

6 

8.73  303 

234 

8.73  366 

234 

11.26  634 

9.99  936 

54 

S 

192        188.0     184 

7 

8.73  535 

232 

8.73  600 

234 

11.26  400 

9.99  936 

53 

9 

216        211.5    207 

8 

8.73  767 

232 

8.73  832 

232 

11.26  168 

9.99  935 

52 

oo  K            ttnn            o  1  c 

9 

8.73  997 

230 
229 

8.74  063 

231 
229 

11.25  937 

9.99  934 

51 

2 

45.0       44.0       43.0 

10 

8.74  226 

8.74  292 

11.25708 

9.99  934 

50 

3 

67.5       66.0       64.5 

11 

8.74  454 

228 

8.74  521 

229 

11.25479 

9.99  933 

49 

4 
5 

90.0      88.0      86.0 
112.5     110.0     107.5 

12 

8.74  680 

226 

8.74  748 

227 

11.25  252 

9.99  932 

48 

6 

135.0     132,0     129.0 

13 
14 

8.74  906 
8.75  130 

226 
224 

223 

8.74  974 
8.75  199 

226 
225 
224 

11.25026 
11.24801 

9.99  932 
9.99  931 

47 
46 

7 
S 
9 

157.5     154.0     150.5 
180.0     176.0     172.0 
202.5     198.0     193.5 

15 

8.75  353 

8.75  423 

11.24  577 

9.99  930 

45 

16 

8.75  575 

222 

8.75  645 

222 

11.24355 

9.99  929 

44 

213         211         208 

17 
18 

8.75  795 
8.76015 

220 
220 

8.75  867 
8.76  087 

222 
220 

11.24  133 
11.23913 

9.99  929 
9.99  928 

43 
42 

2 

3 

4 

42.6       42.2       41.6 
63.9       63.3       62.4 
85.2       84.4       83.2 

19 

8.76  234 

219 

8.76  306 

219 

11.23  694 

9.99  927 

41 

5 

106.5     105.5     104.0 

217 

219 

6 

127  8     126  6     124  8 

20 

8.76  451 

8.76  525 

11.23475 

9.99  926 

40 

7 

149.1     147.7     145.6 

21 

8.76  667 

216 

8.76  742 

217 

11.23258 

9.99  926 

39 

8 

170.4     168.8     166.4 

22 

8.76  883 

216 

8.76  958 

216 

11.23042 

9.99  925 

38 

9 

191.7     189.9     187.2 

23 

8.77  097 

214 

8.77  173 

215 

11.22827 

9.99  924 

37 

one          ono          on* 

24 

8.77310 

213 
212 

8.77  387 

214 
213 

11.22613 

9.99  923 

36 

2 

41.2       40.6       40.2 

25 

8.77  522 

8.77  600 

11.22400 

9.99  923 

35 

3 

61.8       60.9       60.3 

26 

8.77  733 

211 

8.77811 

211 

11.22  189 

9.99  922 

34 

4 
5 

82.4       81.2       80.4 
103.0     101  5     100  5 

27 

8.77  943 

210 

8.78  022 

211 

11.21978 

9.99  921 

33 

6 

123.6     121.8     120.6 

28 
29 

8.78  152 
8.78  360 

209 
208 
208 

8.78  232 
8.78  441 

210 
209 
208 

11.21  768 
11.21  559 

9.99  920 
9.99  920 

32 
31 

8 
9 

144.2     142.1     140.7 
164.8     162.4     160.8 
185.4     182.7     180.9 

30 

8.78  568 

8.78  649 

11.21351 

9.99  919 

30 

31 

8.78  774 

206 

8.78  855 

206 

11.21  145 

9.99  918 

29 

199        197        195 

32 

33 

8.78  979 
8.79  183 

205 
204 

8.79  061 
8.79  266 

206 
205 

11.20939 
11.20734 

9.99  917 
9.99  917 

28 
27 

2 

3 
4 

39.8       39.4       39.0 
59.7       59.1       58.5 
79.6       78.8       78.0 

34 

8.79  386 

203 
202 

8.79  470 

204 

11.20  530 

9.99  916 

26 

5 
6 

99.5       98.5       97.5 
119  4     118  2     117  0 

35 

8.79  588 

8.79  673 

11.20  327 

9.99  915 

25 

7 

139.3     137i9     136'.5 

36 
37 

8.79  789 
8.79  990 

201 
201 

8.79  875 
8.80  076 

202 
201 

11.20125 
11.19924 

9.99  914 
9.99  913 

24 
23 

8 
9 

159.2     157.6     156.0 
179.1     177.3     175.5 

38 

8.80  189 

199 

8.80  277 

201 

11.19723 

9.99  913 

22 

1Q3            1Q2            1QH 

39 

8.80  388 

197 

8.80  476 

199 
198 

11.19524 

9.99  912 

21 

2 

38.6       38.4       38.0 

40 

8.80  585 

8.80  674 

11.19  326 

9.99911 

20 

3 

57.9       57.6       57.0 

41 

8.80  782 

197 

8.80  872 

198 

11.19  128 

9.99  910 

19 

4 
5 

77.2       76.8       76.0 
96  5       96  0       95  0 

42 

8.80  978 

196 

8.81  068 

196 

11.18932 

9.99  909 

18 

6 

115.8     115.2     114.0 

43 

44 

8.81  173 
8.81  367 

195 
194 
193 

8.81  264 
8.81  459 

196 
195 
194 

11.18736 
11.18541 

9.99  909 
9.99  908 

17 
16 

7 
8 
9 

135.1     134.4     133.0 
154.4     153.6     152.0 
173.7     172.8     171.0 

45 

8.81  560 

8.81  653 

11.18347 

9.99  907 

15 

46 

8.81  752 

192 

8.81  846 

193 

11.18154 

9.99  906 

14 

188         186         184 

47 

8.81  944 

192 

8.82  038 

192 

11.17962 

9.99  905 

13 

2 

37.6       37.2       36.8 

48 

8.82  134 

190 

8.82  230 

192 

11.17770 

9.99  904 

12 

3 
4 

56.4       55.8       55.2 
75.2       74.4       73.6 

49 

8.82  324 

190 

8.82  420 

190 

11.17580 

9.99  904 

11 

5 

94.0       93.0       92.0 

189 

190 

G 

112  8     111  6     110  4 

50 

8.82  513 

8.82  610 

11.17390 

9.99  903 

10 

7 

131.6     130.2     128.8 

51 

52 

8.82  701 
8.82  888 

188 
187 

8.82  799 
8.82  987 

189 
188 

11.17201 
11.17013 

9.99  902 
9.99  901 

9 

8 

8 
9 

150.4     148.8     147.2 
169.2     167.4     165.6 

53 

8.83  075 

187 

8.83  175 

188 

11.16825 

9.99  900 

7 

1H9            1R9            1R1 

54 

8.83  261 

186 
185 

8.83  361 

186 
186 

11.16639 

9.99  899 

6 

2 

36.6       36.4       36.2 

55 

8.83  446 

8.83  547 

11.16453 

9.99  898 

5 

3 

54.9       54.6       54.3 

56 

8.83  630 

184 

8.83  732 

185 

11.16268 

9.99  898 

4 

4 
5 

73.2       72.8       72.4 
91.5       91.0       90.5 

57 

8.83  813 

183 

8.83  916 

184 

11.16084 

9.99  897 

3 

6 

109.8     109.2     108.6 

58 
59 

8.83  996 
8.84  177 

183 
181 
181 

8.84  100 
8.84  282 

184 
182 
182 

11.15900 
11.15718 

9.99  896 
9.99  895 

2 
1 

7 
S 
9 

128.1     127.4     126.7 
146.4     145.6     144.8 
164.7     163.8     162.9 

60 

8.84  358 

8.84  464 

11.15536 

9.99  894 

0 

L  Cos 

d 

L  Ctn 

cd 

L  Tan 

LSin 

' 

Prop.  Pts. 

86°  —  Logarithms  of  Trigonometric  Functions 


4°  —  Logarithms  of  Trigonometric  Functions 


[HI 


' 

LSin 

d 

LTan 

cd 

L  Ctn 

LCos 

Prop.  Pts. 

0 

8.84  358 

8.84  464 

11.15536 

9.99  894 

60 

1 

8.84  539 

181 

8.84  646 

182 

11.15354 

9.99  893 

59 

181        180        179 

2 

8.84  718 

179 

8.84  826 

180 

11.15  174 

9.99  892 

58 

2 

36.2       36.0       35.8 

3 

8.84  897 

179 

8.85  006 

180 

11.14994 

9.99  891 

57 

3 

4 

54.3       54.0       53.7 
72.4       72.0       71.6 

4 

8.85  075 

178 

8.85  185 

179 

11.14815 

9.99  891 

56 

5 

90.5       90.0       89.5 

177 

178 

6 

108  6     108  0     107  4 

5 

8.85  252 

8.85  363 

11.14637 

9.99  890 

55 

7 

126.'7     126X)     12513 

6 

8.85  429 

177 

8.85  540 

177 

11.14460 

9.99  889 

54 

8 

144.8     144.0     143.2 

7 

8.85  605 

176 

8.85  717 

177 

11.14283 

9.99  888 

53 

9 

162.9     162.0     161.1 

8 

8.85  780 

175 

8.85  893 

176 

11.14107 

9.99  887 

52 

9 

8.85  955 

175 
173 

8.86  069 

176 
174 

11.13931 

9.99  886 

51 

2 

xii           x  i  o          x  i  a 

35.4      35.0      34.6 

10 

8.86  128 

8.86  243 

11.13757 

9.99  885 

50 

3 

53.1       52.5       51.9 

11 

8.86  301 

173 

8.86  417 

174 

11.13583 

9.99  884 

49 

4 
5 

70.8       70.0       69.2 
88  5       87  5       86  5 

12 

8.86  474 

173 

8.86  591 

174 

11.13409 

9.99  883 

48 

6 

106.2     105.0     103.3 

13 
14 

8.86  645 
8.86  816 

171 
171 
171 

8.86  763 
8.86  935 

172 
172 
171 

11.13237 
11.13  065 

9.99  882 
9.99  881 

47 
46 

8 
9 

123.9     122.5     121.1 
141.6     140.0     138.4 
159.3     157.5     155.7 

15 

8.86  987 

8.87  106 

11.12  894 

9.99  880 

45 

16 

8.87  156 

169 

8.87  277 

171 

11.12723 

9.99  879 

44 

171         170         169 

17 

8.87  325 

169 

8.87  447 

170 

11.12553 

9.99  879 

43 

2 

34.2       34.0       33.8 

18 

8.87  494 

169 

8.87  616 

169 

11.12384 

9.99  878 

42 

3 

4 

51.3       51.0       50.7 
68.4       68.0       67.6 

19 

8.87  661 

167 

8.87  785 

169 

11.12215 

9.99  877 

41 

5 

85.5       85.0       84.5 

168 

168 

102  6     102  0     101  4 

20 

8.87  829 

8.87  953 

11.12047 

9.99  876 

40 

7 

119>     119'.0     118.3 

21 

8.87  995 

166 

8.88  120 

167 

11.11880 

9.99  875 

39 

8 

136.8     136.0     135.2 

22 

8.88  161 

166 

8.88  287 

167 

11.11713 

9.99  874 

38 

9 

153.9     153.0     152.1 

23 

8.88  326 

165 

8.88  453 

166 

11.11547 

9.99  873 

37 

1  AT             1AR             1AQ 

24 

8.88  490 

164 
164 

8.88  618 

165 
165 

11.11382 

9.99  872 

36 

2 

33.4       33.0       32.6 

25 

8.88  654 

8.88  783 

11.11217 

9.99  871 

35 

3 

50.1        49.5       48.9 

26 

8.88  817 

163 

8.88  948 

165 

11.11052 

9.99  870 

34 

4 
5 

66.8       66.0       65.2 
835       825       81.5 

27 

8.88  980 

163 

8.89  111 

163 

11.10889 

9.99  869 

33 

6 

100.2       99.0       97.8 

28 
29 

8.89  142 
8.89  304 

162 
162 

8.89  274 
8.89  437 

163 
163 

11.10726 
11.10663 

9.99  868 
9.99  867 

32 
31 

7 
8 
9 

116.9     115.5     114.1 
133.6     132.0     130.4 
150.3     148.5     146.7 

30 

8.89  464 

160 

8.89  598 

161 

11.10402 

9.99  866 

30 

31 

8.89  625 

161 

8.89  760 

162 

11.10240 

9.99  865 

29 

161         160         169 

32 
33 

8.89  784 
8.89  943 

159 
159 

8.89  920 
8.90  080 

160 
160 

11.10080 
11.09920 

9.99  864 
9.99  863 

28 
27 

2 
3 

4 

32.2       32.0       31.8 
48.3       48.0       47.7 
64.4       64.0       63.6 

34 

8.90  102 

159 

8.90  240 

160 

11.09760 

9.99  862 

26 

5 

80.5      80.0      79.5 

158 

159 

6 

96  6       96  0       95  4 

35 

8.90  260 

8.90  399 

11.09601 

9.99  861 

25 

7 

112>     112.0     111.3 

36 

37 

8.90417 
8.90  574 

157 
157 

8.90  557 
8.90  715 

158 
158 

11.09443 
11.09  285 

9.99  860 
9.99  859 

24 
23 

8 
9 

128.8     128.0     127.2 
144.9     144.0     143.1 

38 

8.90  730 

156 

8.90  872 

157 

11.09  128 

9.99  858 

22 

1  K7            1KB            1  K9 

39 

8.90  885 

155 
155 

8.91  029 

157 
156 

11.08971 

9.99  857 

21 

2 

31.4       31.0       30.6 

40 

8.91  040 

8.91  185 

11.08815 

9.99  856 

20 

3 

47.1       46.5       45.9 

41 

8.91  195 

155 

8.91  340 

155 

11.08660 

9.99  855 

19 

4 
5 

62.8       62.0       61.2 
78.5       77.5       76.5 

42 

8.91  349 

154 

8.91  495 

155 

11.08505 

9.99  854 

18 

6 

94.2       93.0       91.8 

43 

8.91  502 

153 

8.91  650 

155 

11.08350 

9.99  853 

17 

7 
g 

109.9     108.5     107.1 
125  A     124  0     122  4 

44 

8.91  655 

153 

8.91  803 

153 

11.08197 

9.99  852 

16 

9 

141u»     139^5     137.'7 

45 

8.91  807 

152 

8.91  957 

154 

11.08  043 

9.99  851 

15 

46 

8.91  959 

152 

8.92  110 

153 

11.07890 

9.99  850 

14 

151         150         149 

47 

8.92  110 

151 

8.92  262 

152 

11.07738 

9.99  848 

13 

2 
3 

30.2       30.0       29.8 
45  3       45  0       44  7 

48 

8.92  261 

151 

8.92  414 

152 

11.07586 

9.99  847 

12 

4 

60^4       60'.0       59'.6 

49 

8.92411 

150 

8.92  565 

151 

11.07435 

9.99  846 

11 

5 

75.5       75.0       74.5 

150 

151 

6 

90.6       90.0       89.4 

50 

8.92  561 

8.92  716 

11.07284 

9.99  845 

10 

7 

105.7     105.0     104.3 

51 
52 

8.92  710 
8.92  859 

149 
149 

8.92  866 
8.93  016 

150 
150 

11.07  134 
11.06984 

9.99  844 
9.99  843 

9 
8 

8 
9 

120.8     120.0     119.2 
135.9     135.0     134.1 

53 

8.93  007 

148 

8.93  165 

149 

11.06835 

9.99842. 

7 

147          145          144 

54 

8.93  154 

147 

14.7 

8.93  313 

148 

1  4.Q 

11.06687 

9.99  841 

6 

2 

29.4       29.0       28.8 

55 

8.93  301 

XT:/ 

8.93  462 

J.*±<7 

11.06538 

9.99  840 

5 

3 

44.1       43.5       43.2 

56 

8.93  448 

147 

8.93  609 

147 

11.06391 

9.99  839 

4 

4 
5 

58.8       58.0       57.6 
73.5       72.5       72.0 

57 

8.93  594 

146 

8.93  756 

147 

11.06244 

9.99  838 

3 

6 

88.2       87.0       86.4 

58 

8.93  740 

146 

8.93  903 

147 

11.06097 

9.99  837 

2 

7 
g 

102.9     101.5     100.8 
117  6     116  0     115  2 

59 

8.93  885 

145 

145 

8.94  049 

146 
146 

11.05951 

9.99  836 

1 

9 

132'.3     130'.5     129.6 

60 

8.94  030 

8.94  195 

11.05805 

9.99  834 

0 

LCos 

d 

LCtn 

cd 

LTan 

LSin 

' 

Prop.  Pts. 

85°  —  Logarithms  of  Trigonometric  Functions 


Ill]          5°  —  Logarithms  of  Trigonometric  Functions 


51 


' 

LSin 

d 

LTan 

cd 

LCtn 

L  Cos 

Prop.  Pts. 

0 

8.94  030 

8.94  195 

11.05805 

9.99  834 

60 

1 

8.94  174 

144 

8.94  340 

145 

11.05  660 

9.99  833 

59 

143        142        141 

2 

8.94  317 

143 

8.94  485 

145 

11.05515 

9.99  832 

58 

2 

28.6       28.4      28.2 

3 

8.94  461 

144 

8.94  630 

145 

11.05370 

9.99  831 

57 

3 

4 

42.9       42.6       42.3 
57.2       56.8       56.4 

4 

8.94  603 

142 

8.94  773 

143 

11.05  227 

9.99  830 

56 

5 

71.5       71.0       70.5 

143 

144 

6 

85  8       85  2       84  6 

5 

8.94  746 

8.94  917 

11.05083 

9.99  829 

55 

7 

100.1       99i4       98'.7 

6 

8.94  887 

141 

8.95  060 

143 

11.04940 

9.99  828 

54 

8 

114.4     113.6     112.8 

7 

8.95  029 

142 

8.95  202 

142 

11.04798 

9.99  827 

53 

9 

128.7     127.8     126.9 

8 

8.95  170 

141 

8.95  344 

142 

11.04  656 

9.99  825 

52 

9 

8.95  310 

140 
140 

8.95  486 

142 
141 

11.04514 

9.99  824 

51 

2 

UW             J.03             J..SO 

28.0      27.8      27.6 

10 

8.95  450 

8.95  627 

11.04  373 

9.99  823 

50 

3 

42.0       41.7       41.4 

11 

8.95  589 

139 

8.95  767 

140 

11.04233 

9.99  822 

49 

4 
5 

56.0       55.6       55.2 
70  0       69  5       69  0 

12 

8.95  728 

139 

8.95  908 

141 

11.04092 

9.99  821 

48 

6 

84.0       83i4       82^8 

13 
14 

8.95  867 
8.96  005 

139 
138 
138 

8.96  047 
8.96  187 

139 
140 
138 

11.03  953 
11.03  813 

9.99  820 
9.99  819 

47 
46 

7 
8 
9 

98.0       97.3       96.6 
112.0     111.2     110.4 
126.0     125.1     124.2 

15 

8.96  143 

8.96  325 

11.03  675 

9.99  817 

45 

16 

8.96  280 

137 

8.96  464 

139 

11.03  536 

9.99  816 

44 

137         136         135 

17 

8.96  417 

137 

8.96  602 

138 

11.03  398 

9.99  815 

43 

2 

3 

tl.t        Z/.Z        ZY.U 
41.1       40  8       40  5 

18 

8.96  553 

136 

8.96  739 

137 

11.03  261 

9.99  814 

42 

4 

54.8       54.4       54.0 

19 

8.96  689 

136 
136 

8.96  877 

138 
136 

11.03  123 

9.99  813 

41 

5 
6 

68.5       68.0       67.5 
82.2       81.6       81.0 

20 

8.96  825 

8.97  013 

11.02  987 

9.99  812 

40 

7 

95.9       95.2       94.5 

21 

22 

8.96  960 
8.97  095 

135 
135 

8.97  150 
8.97  285 

137 
135 

11.02850 
11.02715 

9.99  810 
9.99  809 

39 
38 

8 
9 

109.6     108.8     108.0 
123.3     122.4     121.5 

23 

8.97  229 

134 

8.97  421 

136 

11.02579 

9.99  808 

37 

134          133         132 

24 

8.97  363 

134 

8.97  556 

135 

11.02444 

9.99  807 

36 

2 

26.8      26.6      26.4 

25 

26 

8.97  496 
8.97  629 

133 

8.97  691 
8.97  825 

135 
134 

11.02  309 
11.02175 

9.99  806 
9.99  804 

35 

34 

3 
4 
5 

40.2       39.9       39.6 
53.6       53.2       52.8 
67.0       66.5       66.0 

27 

8.97  762 

133 

8.97  959 

134 

11.02041 

9.99  803 

33 

6 

80.4       79.8       79.2 

28 

8.97  894 

132 

8.98  092 

133 

11.01  908 

9.99  802 

32 

7 
8 

93.8      93.1       92.4 
107.2     106  4     105  6 

29 

8.98  026 

132 
131 

8.98  225 

133 
133 

11.01  775 

9.99  801 

31 

9 

120.6     119.7     118.8 

30 

8.98  157 

8.98  358 

11.01  642 

9.99  800 

30 

31 

8.98  288 

131 

8.98  490 

132 

11.01510 

9.99  798 

29 

131        130        129 

32 

8.98  419 

131 

8.98  622 

132 

11.01  378 

9.99  797 

28 

2 

3 

ZO.Z        26.U        Z5.8 
39  3       39  0       38  7 

33 

8.98  549 

130 

8.98  753 

131 

11.01  247 

9.99  796 

27 

4 

52  A       52.Q       51>> 

34 

8.98  679 

130 

8.98  884 

131 

11.01  116 

9.99  795 

26 

5 

g 

65.5       65.0       64.5 
78.6       78  0       77  4 

35 

8.98  808 

8.99  015 

11.00985 

9.99  793 

25 

7 

9l!7      9l!o      90!3 

36 
37 

8.98  937 
8.99  066 

129 
129 

8.99  145 
8.99  275 

130 
130 

11.00855 
11.00725 

9.99  792 
9.99  791 

24 
23 

8 
9 

104.8     104.0     103.2 
117.9     117.0     116.1 

38 

8.99  194 

128 

8.99  405 

130 

11.00595 

9.99  790 

22 

1S«           197           19.R 

39 

8.99  322 

128 
128 

8.99  534 

129 

11.00466 

9.99  788 

21 

2 

25.6      25.4      25.2 

40 
41 

8.99  450 
8.99  577 

127 

8.99  662 
8.99  791 

129 

11.00  338 
11.00209 

9.99  787 
9.99  786 

20 

19 

3 
4 
5 

38.4      38.1       37.8 
51.2       50.8       50.4 
64.0       63.5       63.0 

42 

8.99  704 

127 

8.99  919 

128 

11.00081 

9.99  785 

18 

6 

76.8       76.2       75.6 

43 
44 

8.99  830 
8.99  956 

126 
126 
126 

9.00  046 
9.00  174 

127 
128 
127 

10.99  954 
10.99  826 

9.99  783 
9.99  782 

17 
16 

7 
8 
9 

89.6       88.9       88.2 
102.4     101.6     100.8 
115.2     114.3     113.4 

45 

9.00  082 

9.00  301 

10.99  699 

9.99  781 

15 

46 

9.00  207 

125 

9.00  427 

126 

10.99  573 

9.99  780 

14 

126        124        123 

47 
48 

9.00  332 
9.00  456 

125 
124 

9.00  553 
9.00  679 

126 
126 

10.99  447 
10.99  321 

9.99  778 
9.99  777 

13 
12 

2 

3 

4 

25.0       24.8       24.6 
37.5       37.2       36.9 
50.0       49.6       49.2 

49 

9.00  581 

125 
123 

9.00  805 

126 

10.99  195 

9.99  776 

11 

5 
6 

62.5       62.0       61.5 
75.0       74.4       73.8 

50 

9.00  704 

9.00  930 

10.99  070 

9.99  775 

10 

87.5       86.8       86.1 

51 

52 

9.00  828 
9.00  951 

124 
123 

9.01  055 
9.01  179 

125 
124 

10.98  945 
10.98  821 

9.99  773 
9.99  772 

9 

8 

8 
9 

100.0       99.2       98.4 
112.5     111.6     110.7 

53 

9.01  074 

123 

9.01  303 

124 

10.98  697 

9.99771 

7 

195            151            15« 

54 

9.01  196 

122 
122 

9.01  427 

124 
123 

10.98  573 

9.99  769 

6 

2 

24.4      24.2      24.0 

55 

56 

9.01  318 
9.01  440 

122 

9.01  550 
9.01  673 

123 

10.98  450 
10.98  327 

9.99  768 
9.99  767 

5 

4 

3 
4 
5 

36.6       36.3       36.0 
48.8       48.4       48.0 
61.0       60.5       60.0 

57 

9.01  561 

121 

9.01  796 

123 

10.98  204 

9.99  765 

3 

6 

73.2       72.6       72.0 

58 

9.01  682 

121 

9.01  918 

122 

10.98  082 

9.99  764 

2 

7 

85.4       84.7       84.0 
97  6       96  8       96  0 

59 

9.01  803 

121 

9.02  040 

122 

10.97  960 

9.99  763 

1 

9 

109'.8     108'.9     108.0 

60 

9.01  923 

9.02  162 

122 

10.97  838 

9.99  761 

0 

LCos 

d 

LCtn 

cd 

L  Tan 

LSin 

' 

Prop.  Pts. 

84°  —  Logarithms  of  Trigonometric  Functions 


52 


6°  —  Logarithms  of  Trigonometric  Functions  [III 


' 

LSin 

d 

LTan 

cd 

LCtn 

LCos 

Prop.  Pts. 

0 

9.01  923 

9.02  162 

10.97  838 

9.99  761 

60 

1 

9.02  043 

120 

9.02  283 

121 

10.97717 

9.99  760 

59 

121          120         119 

2 

9.02  163 

120 

9.02  404 

121 

10.97  596 

9.99  759 

58 

3 

24.2         24.  U         23.8 

36.3       36.0       35.7 

3 

9.02  283 

120 

9.02  525 

121 

10.97  475 

9.99  757 

57 

4 

48.4       48.0       47.6 

4 

9.02  402 

119 

1  1  Q 

9.02  645 

120 

10.97  355 

9.99  756 

56 

a 

6 

60.5       60.0       59.5 
72.6       72.0       71.4 

5 

9.02  520 

llo 

9.02  766 

10.97  234 

9.99  755 

55 

7 

6 

9.02  639 

119 

9.02  885 

119 

10.97  115 

9.99  753 

54 

8 
9 

96!8       96.0       95.2 
ins  a    ins  n    in?  i 

7 

9.02  757 

118 

9.03  005 

120 

10.96  995 

9.99  752 

53 

8 

9.02  874 

117 

9.03  124 

119 

10.96  876 

9.99  751 

52 

11H            117            11A 

9 

9.02  992 

118 
117 

9.03  242 

118 
119 

10.96  758 

9.99  749 

51 

2 

23.6       23.4       23.2 

10 

9.03  109 

9.03  361 

10.96  639 

9.99  748 

50 

3 

35.4       35.1       34.8 

11 

9.03  226 

117 

9.03  479 

118 

10.96  521 

9.99  747 

49 

4 

47.2       46.8       46.4 
59.0       58.5       58.0 

12 

9.03  342 

116 

9.03  597 

118 

10.96  403 

9.99  745 

48 

6 

70.8       70.2       69.6 

13 

9.03  458 

116 

9.03  714 

117 

10.96  286 

9.99  744 

47 

7 
8 

82.6      81.9      81.2 
94.4       93.6       92.8 

14 

9.03  £74 

116 

9.03  832 

118 

10.96  168 

9.99  742 

46 

9 

106.2     10513     104!4 

15 

9.03  690 

116 

9.03  948 

116 

10.96  052 

9.99  741 

45 

16 

9.03  805 

115 

9.04  065 

117 

10.95  935 

9.99  740 

44 

116        114        113 

17 

9.03  920 

115 

9.04  181 

116 

10.95  819 

9.99  738 

43 

2 

23.0       22.8       22.6 

18 

9.04  034 

114 

9.04  297 

116 

10.95  703 

9.99  737 

42 

3 

4 

34.5       34.2       33.9 
46  0       45  6       45  2 

19 

9.04  149 

115 

9.04  413 

116 

10.95  587 

9.99  736 

41 

5 

57.5       57.0       56.5 

20 

9.04  262 

113 

9.04  528 

115 

10.95  472 

9.99  734 

40 

6 
7 

69.0       68.4       67.8 
80.5       79.8       79.1 

21 

9.04  376 

114 

9.04  643 

115 

10.95  357 

9.99  733 

39 

8 

92.0       91.2       90.4 

22 

9.04  490 

114 

9.04  758 

115 

10.95  242 

9.99  731 

38 

9 

103.5     102.6     101.7 

23 

9.04  603 

113 

9.04  873 

115 

10.95  127 

9.99  730 

37 

24 

9.04715 

112 

9.04  987 

114 

10.95  013 

9.99  728 

36 

112        111        110 

113 

114 

2 

22  4        22  2        22  0 

25 

9.04  828 

9.05  101 

10.94  899 

9.99  727 

35 

3 

33.6       33.3       33.0 

26 

9.04  940 

112 

9.05214 

113 

10.94  786 

9.99  726 

34 

4 

44.8       44.4       44.0 

27 

9.05  052 

112 

9.05  328 

114 

10.94  672 

9.99  724 

33 

5 
6 

56.0       55.5       55.0 
67.2       66.6       66.0 

28 

9.05  164 

112 

9.05  441 

113 

10.94  559 

9.99  723 

32 

7 

78.4      77.7      77.0 

29 

9.05  275 

111 
111 

9.05  553 

112 
113 

10.94  447 

9.99  721 

31 

8 
9 

89.6       88.8       88.0 
100.8      99.9      99.0 

30 

9,05  386 

9.05  666 

10.94  334 

9.99  720 

30 

31 

9.05  497 

111 

9.05  778 

112 

10.94  222 

9.99  718 

29 

109        108        107 

32 

9.05  607 

110 

9.05  890 

112 

10.94  110 

9.99717 

28 

2 

21.8       21.6       21.4 

33 

9.05  717 

110 

9.06  002 

112 

10.93  998 

9.99  716 

27 

3 

32.7       32.4       32.1 

34 

9.05  827 

110 
1  1  r\ 

9.06  113 

111 

10.93  887 

9.99  714 

26 

4 
5 

43.6       43.2       42.8 
54.5       54.0       53.5 

35 

36 

9.05  937 
9.06  046 

1IU 

109 

9.06  224 
9.06  335 

111 

10.93  776 
10.93  665 

9.99  713' 
9.99  711 

25 

24 

e 

7 
8 

65.4       64.8       64.2 
76.3       75.6       74.9 
87.2       86.4       85.6 

37 

9.06  155 

109 

9.06445 

110 

10.93  555 

9.99  710 

23 

9 

98.1      97.2      96.3 

88 

9.06  264 

109 

9.06  556 

111 

10.93  444 

9.99  708 

22 

39 

9.06  372 

108 

9.06  666 

110 

10.93  33t 

9.99  707 

21 

106        105        104 

40 

9.06  481 

109 

9.06  775 

109 

10.93  225 

9.99  705 

20 

2 
3 

21.2      21.0       20.8 
31  8       31  5       31  2 

41 

9.06  589 

108 

9.06  885 

110 

10.93  115 

9.99  704 

19 

4 

42'.4       42io       4L6 

42 

9.06  696 

107 

9.06  994 

109 

10.93  006 

9.99  702 

18 

5 

53.0       52.5       62.0 

43 

9.06  804 

108 

9.07  103 

109 

10.92  897 

9.99  701 

17 

6 

7 

63.6       63.0       62.4 
74  2       73.5       72.8 

44 

9.06911 

107 

9.07211 

108 

10.92  789 

9.99  699 

16 

8 

84.8       84.0       83.2 

45 

9.07  018 

107 

9.07  320 

109 

10.92  680 

9.99  698 

15 

9 

95.4       94.5       93.6 

46 
47 

9.07  124 
9.07  231 

106 
107 

9.07  428 
9.07  536 

108 
108 

10.92  572 
10.92  464 

9.99  696 
9.99  695 

14 
13 

From  the  top: 

48 

9.07  337 

106 

9.07  643 

107 

10.92  357 

9.99  693 

12 

For  60+  or  186°+, 

49 

9.07  442 

105 
106 

9.07  751 

108 
107 

10.92  249 

9.99  692 

11 

read  as  printed;  for 

50 

51 

9.07  548 
9.07  653 

105 

9.07  858 
9.07  964 

106 

10.92  142 
10.92  036 

9.99  690 
9.99  689 

10 

9 

960-1-  or  276°+,  read 

52 

9.07  758 

105 

9.08071 

107 

10.91  929 

9.99  687 

8 

co-function. 

53 

9.07  863 

105 

9.08  177 

106 

10.91  823 

9.99  686 

7 

54 

9.07  968 

105 

9.08  283 

106 

10.91717 

9.99  684 

6 

From  the  bottom: 

55 

56 
57 

9.08  072 
9.08  176 
9.08  280 

104 
104 
104 

9.08  389 
9.08  495 
9.08  600 

106 
106 
105 

10.91  611 
10.91  505 
10.91  400 

9.99  683 
9.99  681 
9.99  680 

5 

4 
3 

For  83°+  or  263°+ 

read  as  printed;  for 

58 

9.08  383 

103 

9.08  705 

105 

10.91  295 

9.99  678 

2 

173°+  or  353°+,  read 

59 

9.08  486 

103 
103 

9.08810 

105 
104 

10.91  190 

9:99-677- 

1 

co-function. 

60 

9.08  589 

9.08  914 

10.91  086 

9.99  675 

0 

LCos 

d 

LCtn 

cd 

LTan 

LSin 

' 

Prop.  Pts. 

83°  —  Logarithms  of  Trigonometric  Functions 


Ill]          7°  —  Logarithms  of  Trigonometric  Functions 


53 


' 

LSin 

d 

L  Tan 

cd 

LCtn 

LCos 

Prop.  Pts. 

0 

9.08  589 

9.08  914 

10.91  086 

9.99  675 

60 

1 

9.08  692 

103 

9.09  019 

105 

10.90  981 

9.99  674 

59 

2 

9.08  795 

103 

9.09  123 

104 

10.90  877 

9.99  672 

58 

105        104        103 

3 

9.08  897 

102 

9.09  227 

104 

10.90  773 

9.99  670 

57 

2 

21.0     20.8      20.6 

4 

9.08  999 

102 

9.09  330 

103 

1  A.1 

10.90  670 

9.99  669 

56 

3 
4 

31.5      31.2      30.9 
42.0      41.6      41.2 

5 

9.09  101 

102 

9.09  434 

1O1 

10.90  566 

9.99  667 

55 

5 

• 

52.5      52.0      51.5 
63.0      62  4      61  8 

6 

9.09  202 

101 

9.09  537 

103 

10.90  463 

9.99  666 

54 

7 

73^5      72^8      72!l 

7 

9.09  304 

102 

9.09  640 

103 

10.90  360 

9.99  664 

53 

8 

84.0      83.2      82.4 

8 

9.09  405 

101 

9.09  742 

102 

10.90  258 

9.99  663 

52 

9 

94.5      93.6      92.7 

9 

9.09  506 

101 

9.09  845 

103 

10.90  155 

9.99  661 

51 

10 

9.09  606 

100 

9.09  947 

102 

10.90  053 

9.99  659 

50 

102         101           99 

11 

9.09  707 

101 

9.10  049 

102 

1  At 

10.89  951 

9.99  658 

49 

2 

20.4      20.2      19.8 

12 

9.09  807 

100 

9.10  150 

1U1 

10.89  850 

9.99  656 

48 

3 

30.6      30.3      29.7 

13 
14 

9.09  907 
9.10006 

100 
99 

9.10  252 
9.10  353 

102 
101 

10.89  748 
10.89  647 

9.99  655 
9.99  653 

47 
46 

4 
5 
6 

40.8      40.4      39.6 
51.0      50.5      49.5 
61.2      60.6      59.4 

15 

9.10  106 

100 

9.10  454 

101 

10.89  546 

9.99  651 

45 

7 
8 

71.4      70.7      C9.3 
81  6      80  8      79  2 

16 

9.10  205 

99 

9.10  555 

101 

10.89  445 

9.99  650 

44 

9 

91.8      90.9      89.1 

17 

9.10  304 

99 

9.10  656 

101 

10.89  344 

9.99  648 

43 

18 

9.10  402 

98 

9.10756 

100 

10.89  244 

9.99  647 

42 

19 

9.10501 

99 

9.10  856 

100 

10.89  144 

9.99  645 

41 

98          97          96 

20 

21 

9.10  599 
9.10  697 

98 
98 

9.10  956 
9.11  056 

100 
100 

10.89  044 
10.88  944 

9.99  643 
9.99  642 

40 

39 

2 
3 
4 

19.6      19.4      19.2 
29.4      29.1      28.8 
39.2      38.8      38.4 

22 

9.10  795 

98 

9.11  155 

99 

10.88  845 

9.99  640 

38 

5 

49.0      48.5      48.0 

23 

9.10  893 

98 

9.11  254 

99 

10.88  746 

9.99  638 

37 

6 

58.8      58.2      57.6 
68  6      67  9      67  2 

24 

9.10  990 

97 

9.11  353 

99 

10.88  647 

9.99  637 

36 

8 

78.'4      77^6      76.8 

25 

9.11  087 

97 

9.11  452 

99 

10.88  548 

9.99  635 

35 

9 

83.2      87.3      86.4 

26 

9.11  184 

97 

9.11551 

99 

10.88  449 

9.99  633 

34 

27 

9.11  281 

97 

9.11  649 

98 

10.88  351 

9.99  632 

33 

28 

9.11  377 

96 

9.11  747 

98 

10.88  253 

9.99  630 

32 

95          94          93 

29 

9.11  474 

97 

Qfi 

9.11  845 

98 
98 

10.88  155 

9.99  629 

31 

2 
3 

19.U        18.8        1S.C 
28.5      28.2      27.9 

30 

31 

9.11  570 
9.11  666 

*7U 

96 

9.11  943 
9.12  040 

97 

10.88  057 
10.87  960 

9.99  627 
9.99  625 

30 

29 

4 
5 
6 

38.0      37.6      37.2 
47.5      47.0      46.5 
57.0      56.4      55.8 

32 

9.11  761 

95 

9.12  138 

98 

10.87  862 

9.99  624 

28 

7 

66.5      65.8      65.1 

33 

9.11  857 

96 

9- 

9.12  235 

97 

10.87  765 

9.99  622 

27 

8 
9 

76.0      75.2      74.4 
85.5      84.6      83.7 

34 

9.11  952 

o 

9.12  332 

97 

10.87  668 

9.99  620 

26 

35 

9.12  047 

95 

9.12  428 

96 

10.87  572 

9.99  618 

25 

36 

9.12  142 

95 

9.12  525 

97 

10.87  475 

9.99  617 

24 

92           91          90 

37 

9.12  236 

94 

9.12621 

96 

10.87  379 

9.99  615 

23 

2 

18.4      18.2      18.0 

38 
39 

9.12  331 
9.12  425 

95 
94 

9.12717 
9.12813 

96 
96 

OA 

10.87  283 
10.87  187 

9.99  613 
9.99  612 

22 
21 

3 
4 
5 

27.6      27.3      27.0 
36.8      36.4      36.0 
46.0      45.5      45.0 

40 

9.12519 

94 

9.12  909 

yo 

10.87  091 

9.99  610 

20 

6 
7 

55.2      64.6      54.0 
64  4      63.7      63.0 

41 

9.12  612 

93 

9.13  004 

yo 

10.86  996 

9.99  608 

19 

8 

73^6      72.8      72.0 

42 

9.12  706 

94 

9.13  099 

95 

10.86  901 

9.99  607 

18 

9 

82.8      81.9      81.0 

43 

9.12799 

93 

9.13  194 

95 

10.86  806 

9.99  605 

17 

44 

9.12  892 

93 

9.13  289 

95 

10.86711 

9.99  603 

16 

45 

9.12  985 

93 

9.13  384 

95 

10.86  616 

9.99  601 

15 

From  the  top: 

46 

9.13  078 

93 

9.13  478 

94 

9e 

10.86  522 

9.99  600 

14 

For  70+  or  187°+, 

47 

48 

9.13  171 
9.13  263 

93 
92 

9.13  573 
9.13  667 

0 

94 

10.86  427 
10.86  333 

9.99  598 
9.99  596 

13 
12 

read  as  printed;  for 

49 

9.13  355 

92 

9.13761 

94 

10.86  239 

9.99  595 

11 

970+  or  2770+,  read 

50 

9.13  447 

92 

9.13  854 

93 

10.86  146 

9.99  593 

10 

co-function. 

51 

9.13  539 

92 

9.13  948 

94 

10.86  052 

9.99  591 

9 

52 

9.13  630 

91 

9.14  041 

93 

10.85  959 

9.99  589 

8 

53 

9.13  722 

92 

9.14  134 

93 

10.85  866 

9.99  588 

7 

From  the  bottom: 

54 
55 
56 

9.13  813 
9.13  904 
9.13  994 

91 
91 
90 

9.14  227 
9.14  320 
9.14412 

93 
93 
92 

10.85  773 
10.85  680 
10.85  588 

9.99  586 
9.99  584 
9.99  582 

6 
5 
4 

For  82°+  or  262°+, 
read  as  printed;  for 

57 

9.14  085 

91 

9.14  504 

92 

10.85  496 

9.99  581 

3 

172°+  or  3520+,  read 

58 

9.14  175 

90 

9.14  597 

93 

10.85  403 

9.99  579 

2 

co-function. 

59 

9.14  266 

91 

9.14  688 

91 

10.85  312 

9.99  577 

1 

60 

9.14  356 

90 

9.14  780 

92 

10.S5  220 

9.99  575 

0 

L  Cos 

d 

L  Ctn 

cd 

L  Tan 

LSin 

' 

Prop.  Pts. 

82°  —  Logarithms  of  Trigonometric  Functions 


54 


8°  —  Logarithms  of  Trigonometric  Functions 


[HI 


/ 

LSin 

d 

LTan 

cd 

LCtn 

LCos 

Prop.  Pts. 

0 

9.14  356 

9.14780 

10.85  220 

9.99  575 

60 

1 

9.14  445 

89 

9.14872 

92 

10.85  128 

9.99  574 

59 

2 

9.14  535 

90 

9.14  963 

91 

10.85  037 

9.99  572 

58 

92 

91 

90 

3 

4 

9.14  624 
9.14714 

89 
90 

89 

9.15  054 
9.15  145 

91 
91 
91 

10.84  946 
10.84  855 

9.99  570 
9.99  568 

57 

56 

2 
3 

18.4 
27.6 

18.2 
27.3 

18.0 
27.0 

5 

9.14  803 

9.15  236 

10.84  764 

9.99  566 

55 

4 

36.8 

36.4 

36.0 

6 

9.14891 

88 

9.15  327 

91 

10.84  673 

9.99  565 

54 

5 

46.0 

45.5 

45.0 

7 

9.14  980 

89 

9.15417 

90 

10.84  583 

9.99  563 

53 

6 

55.2 

54.6 

54.0 

8 

9.15  069 

89 

9.15508 

91 

10.84  492 

9.99  561 

52 

7 

64.4 

63.7 

63.0 

9 

9.15  157 

88 

9.15  598 

90 

10.84  402 

9.99  559 

51 

8 

73.6 

72.8 

72.0 

10 

9.15  245 

88 

9.15  688 

90 

10.84  312 

9.99  557 

50 

9 

82.8 

81.9 

81.0 

11 

9.15  333 

88 

9.15  777 

89 

10.84  223 

9.99  556 

49 

12 

9.15421 

88 

9.15  867 

90 

10.84  133 

9.99  554 

48 

13 

9.15  508 

87 

9.15  956 

89 

10.84  044 

9.99  552 

47 

OB 

00 

BY 

14 

9.15  596 

88 

9.16  046 

90 

10.83  954 

9.99  550 

46 

2 

17.8 

17.6 

17.4 

15 

9.15  683 

87 

9.16  135 

89 

10.83  865 

9.99  648 

45 

3 

26.7 

26.4 

26.1 

16 

9.15  770 

87 

9.16  224 

89 

10.83  776 

9.99  546 

44 

4 

35.6 

35.2 

34.8 

17 

9.15  857 

87 

9.16  312 

88 

10.83  688 

9.99  545 

43 

5 

44.5 

44.0 

43.5 

18 

9.15  944 

87 

9.16401 

89 

10.83  599 

9.99  543 

42 

6 

53.4 

52.8 

52.2 

19 

9.16  030 

86 

9.16  489 

88 

10.83511 

9.99  541 

41 

7 

62.3 

61.6 

60.9 

86 

88 

8 

71.2 

70.4 

69.6 

20 

9.16  116 

9.16  577 

10.83  423 

9.99  539 

40 

g 

80.1 

79.2 

78.3 

21 

9.16  203 

87 

9.16  665 

88 

10.83  335 

9.99  537 

39 

22 

9.16  289 

86 

9.16  753 

88 

10.83  247 

9.99  535 

38 

23 

9.16  374 

85 

9.16  841 

88 

10.83  159 

9.99  533 

37 

86 

85 

84 

24 

9.16  460 

86 
85 

9.16928 

87 
88 

10.83  072 

9.99  532 

36 

2 

17.2 

17.0 

16.8 

25 

9.16  545 

9.17016 

10.82  984 

9.99  530 

35 

3 

25.8 

25.5 

25.2 

2G 

9.16631 

86 

9.17  103 

87 

10.82  897 

9.99  528 

34 

4 

34.4 

34.0 

33.6 

27 

9.16716 

85 

Q  C 

9.17  190 

87 

10.82  810 

9.99  526 

33 

6 

43.0 

42.5 

42.0 

28 

9.16  801 

oo 

9.17  277 

87 

10.82  723 

9.99  524 

32 

6 

51.6 

51.0 

50.4 

29 

9.16  886 

85 
84 

9.17  363 

86 

87 

10.82  637 

9.99  522 

31 

7 

60.2 

59.5 

58.8 

30 

9.16  970 

9.17  450 

10.82  550 

9.99  520 

30 

8 

68.8 

68.0 

67.2 

31 

9.17  055 

85 

9.17  636 

86 

10.82  464 

9.99  518 

29 

9 

77.4 

76.5 

75.6 

32 

*9.17  139 

84 

9.17  622 

86 

10.82  378 

9.99  517 

28 

33 

9.17  223 

84 

9.17  708 

86 

10.82  292 

9.99515 

27 

34 

9.17  307 

84 

9.17  794 

86 

10.82  206 

9.99  513 

26 

83 

82 

81 

35 

9.17  391 

84 

9.17  880 

86 

10.82  120 

9.99  511 

25 

2 

16.6 

16.4 

16.2 

36 

9.17  474 

83 

9.17965 

85 

10.82  035 

9.99  509 

24 

3 

24.9 

24.6 

24.3 

37 

9.17  558 

84 

9.18051 

86 

10.81  949 

9.99  507 

23 

4 

33.2 

32.8 

32.4 

38 

9.17  641 

83 

9.18  136 

85 

10.81  864 

9.99  505 

22 

5 

41.5 

41.0 

40.5 

39 

9.17  724 

83 

9.18221 

85 

10.81  779 

9.99  503 

21 

6 

49.8 

49.2 

48.6 

40 

41 

42 

9.17  807 
9.17  890 
9.17  973 

83 
83 
83 

9.18  306 
9.18  391 
9.18  475 

85 
85 
84 

10.81  694 
10.81  609 
10.81  625 

9.99  501 
9.99  499 
9.99  497 

20 

19 

18 

7 
8 
9 

58.1 
66.4 
74.7 

57.4 
65.6 
73.8 

56.7 
64.8 
72.9 

43 

9.18055 

82 

9.18  560 

85 

10.81  440 

9.99  495 

17 

44 
45 

9.18  137 
9.18  220 

82 
83 

9.18  644 
9.18  728 

84 
84 

10.81  356 
10.81  272 

9.99  494 
9.99  492 

16 
15 

From  the  top: 

46 

9.18  302 

82 

9.18812 

84 

10.81  188 

9.99  490 

14 

For  8°+  or  188°+ 

47 
48 
49 

9.18  383 
9.18  465 
9.18  547 

81 
82 
82 

9.18  896 
9.18  979 
9.19  063 

84 
83 
84 

10.81  104 
10.81  021 
10.80  937 

9.99  488 
9.99  486 
9.99  484 

13 
12 
11 

read   as  printed;   for 
98°+   or   278°+,   read 

50 

9.18  628 

81 

9.19  146 

83 

10.80  854 

9.99  482 

10 

co-function. 

51 

9.18  709 

81 

9.19  229 

83 

10.80771 

9.99  480 

9 

52 
53 

9.18  790 
9.18871 

81 
81 

9.19312 
9.19  395 

83 
83 

10.80  688 
10.80  605 

9.99  478 
9.99  476 

8 

7 

From  the  bottom: 

54 

9.18  952 

81 
81 

9.19478 

83 
83 

10.80  522 

9.99  474 

6 

For  810+  or  261°+, 

55 

56 
57 

9.19  033 
9.19  113 
9.19  193 

80 
80 

9.19  561 
9.19  643 
9.19  725 

82 
82 

10.80  439 
10.80  357 
10.80  275 

9.99  472 
9.99  470 
9.99  468 

5 

4 
3 

read   as  printed;   for 
171°+  or  351°+,  read 

58 

9.19  273 

80 

9.19  807 

82 

10.80  193 

9.99  466 

2 

co-function. 

59 

9.19  353 

80 

9.19  889 

82 

10.80111 

9.99  464 

1 

60 

9.19  433 

80 

9.19  971 

82 

10.80  029 

9.99  462 

0 

LCos 

d 

LCtn 

cd 

LTan 

LSin 

/ 

Prop.  Pts. 

81°  —  Logarithms  of  Trigonometric  Functions 


Ill]          9°  —  Logarithms  of  Trigonometric  Functions 


55 


' 

LSin 

d 

LTan 

cd 

L  Ctn 

L  Cos 

Prop.  Pts. 

0 

9.19433 

9.19  971 

10.80  029 

9.99  462 

60 

1 

9.19513 

80 

9.20  053 

82 

10.79  947 

9.99  460 

59 

2 

9.19  592 

79 

9.20  134 

81 

10.79  866 

9.99  458 

58 

82 

81 

80 

3 

9.19  672 

80 

9.20216 

82 

10.79  784 

9.99  456 

57 

2 

16.4 

16.2 

16.0 

4 

9.19751 

79 

9.20  297 

81 

10.79  703 

9.99  454 

56 

3 

5 

9.19  830 

79 

9.20  378 

81 

10.79  622 

9.99  452 

55 

4 

32.8 

32i4 

32!o 

6 

9.19  909 

79 

9.20  459 

81 

10.79  541 

9.99  450 

54 

5 

41.0 

40.5 

40.0 

7 

9.19  988 

79 

9.20  540 

81 

10.79  460 

9.99  448 

53 

6 

49.2 

48.6 

48.0 

8 

9.20  067 

79 

9.20621 

81 

10.79  379 

9.99  446 

52 

7 

57.4 

56.7 

56.0 

9 

9.20  145 

78 

9.20701 

80 

10.79  299 

9.99  444 

51 

8 

65.6 

64.8 

64.0 

10 

9.20  223 

78 

9.20  782 

81 

10.79  218 

9.99  442 

50 

9 

73.8 

72.9 

72.0 

11 

9.20  302 

79 

9.20  862 

80 

10.79  138 

9.99  440 

49 

12 

9.20  380 

78 

9.20  942 

80 

10.79  058 

9.99  438 

48 

13 

9.20  458 

78 

9.21  022 

80 

10.78  978 

9.99  436 

47 

<» 

70 

It 

14 

9.20  535 

77 

9.21  102 

80 

10.78  898 

9.99  434 

46 

2 

15.8 

15.6 

15.4 

15 

9.20  613 

78 

9.21  182 

80 

10.78  818 

9.99  432 

45 

3 

23.7 

23.4 

23.1 

16 

9.20  691 

78 

9.21  261 

79 

10.78  739 

9.99  429 

44 

4 

31.6 

31.2 

30.8 

17 

9.20  768 

77 

9.21  341 

80 

10.78  659 

9.99  427 

43 

5 

39.5 

39.0 

38.5 

18 

9.20  845 

77 

9.21  420 

79 

10.78  580 

9.99  425 

42 

6 

47.4 

46.8 

46.2 

19 

9.20  922 

77 

9.21  499 

79 

10.78  501 

9.99  423 

41 

7 

55.3 

54.6 

53.9 

20 

21 

9.20  999 
9.21  076 

77 
77 

9.21  578 
9.21  657 

79 
79 

10.78  422 
10.78  343 

9.99  421 
9.99  419 

40 

39 

8 
9 

63.2 
71.1 

62.4 
70.2 

61.6 
69.3 

22 

9.21  153 

77 

9.21  736 

79 

10.78  264 

9.99  417 

38 

23 

9.21  229 

76 

9.21  814 

78 

10.78  186 

9.99  415 

37 

76 

75 

74 

24 

9.21  306 

77 
76 

9.21  893 

79 
78 

10.78  107 

9.99  413 

36 

2 

15.2 

15.0 

14.8 

25 

9.21  382 

9.21  971 

10.78  029 

9.99411 

35 

3 

22.8 

22.5 

22.2 

26 

9.21  458 

76 

9.22  049 

78 

10.77  951 

9.99  409 

34 

4 

30.4 

30.0 

29.6 

27 

9.21  534 

76 

9.22  127 

78 

10.77  873 

9.99  407 

33 

5 

38.0 

37.5 

37.0 

28 

9.21  610 

76 

9.22  205 

78 

10.77  795 

9.99  404 

32 

6 

45  6 

45.0 

44.4 

29 

9.21  685 

75 
76 

9.22  283 

78 
78 

10.77  717 

9.99  402 

31 

7 

53.2 

52.5 

51.8 

30 

9.21  761 

9.22  361 

10.77  639 

9.99  400 

30 

8 

60.8 

60.0 

59.2 

31 

9.21  836 

75 

9.22  438 

77 

10.77  562 

9.99  398 

29 

9 

68.4 

67.5 

66.6 

32 

9.21  912 

76 

9.22  516 

78 

10.77  484 

9.99  396 

28 

33 

9.21  987 

75 

9.22  593 

77 

10.77  407 

9.99  394 

27 

34 

9.22  062 

75 

9.22  670 

77 

10.77  330 

9.99  392 

26 

73 

72 

71 

35 

9.22  137 

75 

9.22  747 

77 

10.77  253 

9.99  390 

25 

2 

14.6 

14.4 

14.2 

36 

9.22211 

74 

9.22  824 

77 

10.77  176 

9.99  388 

24 

3 

21.9 

21.6 

21.3 

37 

9.22  286 

75 

9.22  901 

77 

10.77  099 

9.99  385 

23 

4 

29.2 

28.8 

28.4 

38 

9.22  361 

75 

9.22  977 

76 

10.77  023 

9.99  383 

22 

5 

36.5 

36.0 

35.5 

39 

9.22  435 

74 

9.23  054 

77 

10.76  946 

9.99  381 

21 

6 

43.8 

43.2 

42.6 

40 

9.22  509 

74 

9.23  130 

76 

10.76  870 

9.99  379 

20 

7 

51.1 

50.4 

49.7 

41 

9.22  583 

74 

9.23  206 

76 

10.76  794 

9.99  377 

19 

8 

58.4 

57.6 

56.8 

42 

9.22  657 

74 

9.23  283 

77 

10.76717 

9.99  375 

18 

9 

65.7 

64.8 

63.9 

43 

9.22  731 

74 

9.23  359 

76 

10.76  641 

9.99  372 

17 

44 

9.22  805 

74 

9.23  435 

76 

10.76  565 

9.99  370 

16 

45 

9.22  878 

73 

9.23  510 

75 

10.76  490 

9.99  368 

15 

From  the  top: 

46 

9.22  952 

74 

9.23  586 

76 

10.76414 

9.99  366 

14 

For  9°+,  or  189°+ 

47 
48 
49 

9.23  025 
9.23  098 
9.23  171 

73 
73 

9.23  661 
9.23  737 
9.23  812 

75 
76 
75 

10.76  339 
10.76  263 
10.76  188 

9.99  364 
9.99  362 
9.99  359 

13 
12 
11 

read   as   printed;   for 
99°+   or   279°+    read 

50 

9.23  244 

73 

9.23  887 

75 

10.76  113 

9.99  357 

10 

co-function, 

51 

9.23  317 

73 

9.23  962 

75 

10.76  038 

9.99  355 

9 

52 

9.23  390 

73 

9.24  037 

75 

10.75  963 

9.99  353 

8 

53 

9.23  462 

72 

9.24  112 

75 

10.75  888 

9.99  351 

7 

From  the  bottom: 

54 

9.23  535 

73 
72 

9.24  186 

74 

10.75  814 

9.99  348 

6 

For  80°+  or  260°+, 

55 

56 
57 

9.23  607 
9.23  679 
9.23  752 

72 
73 

9.24  261 
9.24  335 
9.24  410 

74 
75 

10.75  739 
10.75  665 
10.75  590 

9.99  346 
9.99  344 
9.99  342 

5 

4 
3 

read   as   printed;   for 
170°+  or  350°+,  read 

58 

9.23  823 

71 

9.24  484 

74 

10.75  516 

9.99  340 

2 

co-function. 

59 

9.23  895 

72 

9.24  558 

74 

10.75  442 

9.99  337 

1 

60 

9.23  967 

'- 

9.24  632 

74 

10.75  368 

9.99  335 

0 

LCos 

d 

L  On 

cd 

L  Tan 

LSin 

' 

Prop.  Pts. 

80°  —  Logarithms  of  Trigonometric  Functions 


10°  —  Logarithms  of  Trigonometric  Functions          [III 


/ 

LSin 

d 

LTan 

cd 

L  Ctn 

L  Cos 

d 

Prop.  Pts. 

0 

9.23  967 

9.24  632 

10.75  368 

9.99  335 

60 

1 

9.24  039 

72 

9.24  706 

74 

10.75  294 

9.99333 

2 

59 

2 

9.24  110 

71 

9.24  779 

73 

10.75221 

9.99331 

2 

58 

74 

73 

72 

3 

4 

9.24  181 
9.24  253 

71 
72 
71 

9.24  853 
9.24  926 

74 
73 
74 

10.75  147 
10.75  074 

9.99  328 
9.99  326 

3 

2 
2 

57 
56 

2 
3 

14.8 
22.2 

14.6 
21.9 

14.4 
21.6 

5 

9.24  324 

9.25  000 

10.75  000 

9.99  324 

55 

4 

29.6 

29.2 

28.8 

6 

9.24  395 

71 

9.25  073 

73 

10.74  927 

9.99  322 

2 

54 

5 

37.0 

36.5 

36.0 

7 

9.24  466 

9.25  146 

73 

10.74  854 

9.99319 

3 

53 

(i 

44.4 

43.8 

43.2 

8 

9.24  536 

70 

9.25  219 

73 

10.74781 

9.99317 

2 

52 

7 

51.8 

51.1 

50.4 

9 

9.24  607 

71 
70 

9.25  292 

73 
73 

10.74708 

9.99315 

2 
2 

51 

8 

59.2 

58.4 

57.6 

10 

9.24  677 

9.25  365 

10.74  635 

9.99313 

50 

9 

66.6 

65.7 

64.8 

11 

9.24  748 

71 

9.25  437 

72 

10.74563 

9.99310 

3 

49 

12 

9.24  818 

70 

9.25  510 

73 

10.74490 

9.99308 

2 

48 

13 

9.24  888 

70 

9.25  582 

72 

10.74418 

9.99306 

2 

47 

71 

TO 

69 

14 

9.24  958 

70 

9.25  655 

73 

10.74  345 

9.99304 

2 

46 

2 

14.2 

14.0 

13.8 

15 

9.25  028 

70 

9.25  727 

72 

10.74273 

9.99301 

3 

45 

3 

21.3 

21.0 

20.7 

16 

9.25  098 

70 

9.25  799 

72 

10.74201 

9.99299 

2 

44 

4 

28.4 

28.0 

27.6 

17 

9.25  168 

70 

9.25  871 

72 

10.74  129 

9.99297 

2 

43 

0 

35.5 

35.0 

34.5 

18 

9.25237 

69 

9.25  943 

72 

10.74057 

9.99  294 

3 

42 

G 

42.6 

42.0 

41.4 

19 

9.25  307 

70 

9.26  015 

72 

10.73  985 

9.99  292 

2 

41 

7 

49.7 

49.0 

48.3 

69 

71 

2 

g 

56  8 

56.0 

55.2 

20 

21 

9.25  376 
9.25  445 

69 

9.26  086 
9.26  158 

72 

10.73  914 
10.73  842 

9.99  290 
9.99  288 

2 

40 

39 

9 

63'.9 

esio 

62!l 

22 

9.25  514 

69 

9.26  229 

71 

10.73771 

9.99  285 

3 

38 

23 

9.25  583 

69 

9.26301 

72 

10.73  699 

9.99283 

2 

37 

68 

67 

66 

24 

9.25  652 

69 

9.26  372 

71 

10.73  628 

9.99281 

2 

36 

69 

71 

3 

2 

13.6 

13.4 

13.2 

25 

9.25  721 

9.26  443 

10.73  557 

9.99  278 

35 

3 

20.4 

20.1 

19.8 

26 

9.25  790 

69 

fro 

9.26  514 

71 

10.73486 

9.99270 

2 

34 

4 

27.2 

26.8 

26.4 

27 

9.25  858 

OO 
AO 

9.26  585 

10.73415 

9.99  274 

2 

33 

5 

34.0 

33.5 

33.0 

28 

9.25  927 

Da 

£SQ 

9.26  655 

70 

10.73345 

9.99271 

32 

6 

40.8 

40.2 

39.6 

29 

9.25  995 

DO 
68 

9.26  726 

71 
71 

10.73  274 

9.99  209 

2 
2 

31 

7 

47.6 

46.9 

46.2 

30 

9.26  063 

9.26  797 

10.73  203 

9.99  267 

30 

8 

54.4 

53.6 

52.8 

31 

9.26  131 

68 

9.26  867 

70 

10.73  133 

9.99264 

3 

29 

9 

61.2 

60.3 

59.4 

32 

9.26  199 

68 

9.26  937 

70 

10.73  063 

9.99  262 

2 

28 

33 

9.26  267 

68 

9.27  008 

71 

10.72992 

9.99  260 

2 

27 

34 

9.26  335 

68 

9.27  078 

70 

10.72  922 

9.99257 

3 

26 

65 

3 

2 

35 

9.26  403 

68 

o^Tjia. 

70 

10.72852 

9.99  255 

2 

25 

2 

13.0 

0.6 

0.4 

30 

9.26470 

67 

T772T218 

70 

10.72  782 

9.99252 

3 

24 

3 

19.5 

0.9 

0.6 

37 

9.26  538 

68 

9.27  288 

70 

10.72712 

9.99  250 

2 

23 

4 

26.C 

1.2 

0.8 

38 

9.26  605 

67 

9.27  357 

69 

10.72643 

9.99  248 

2 

22 

5 

32.5 

1.5 

1.0 

39 

9.26  672 

67 

9.27  427 

70 

10.72  573 

9.99  245 

3 

21 

6 

39.C 

1.8 

1.2 

40 

9.26  739 

67 

9.27  496 

69 

10.72  504 

9.99  243 

2 

20 

7 

45.5 

2.1 

1.4 

41 

9.26  806 

67 

9.27  566 

70 

10.72434 

9.99241 

2 

19 

8 

52.  ( 

2.4 

1.6 

42 

9.26  873 

67 

9.27  635 

69 

10.72305 

9.99  238 

3 

18 

9 

58.5 

2.7 

1.8 

43 

9.26  940 

67 

9.27  704 

69 

10.72  296 

9.99  236 

2 

17 

44 

9.27  007 

67 

9.27  773 

69 

10.72  227 

9.99  233 

3 

16 

45 

9.27  073 

66 

9.27  842 

69 

10.72  158 

9.99  231 

2 

15 

From  the  top: 

46 

9.27  140 

67 

9.27911 

69 

10.72089 

9.99  229 

2 

14 

ForlO°+orl900+, 

47 
48 
49 

9.27  206 
9.27  273 
9.27  339 

66 
67 
C6 

9.27  980 
9.28  049 
9.28  117 

69 
69 
68 

10.72020 
10.71951 
10.71  883 

9.99  226 
9.99  224 
9.99221 

3 

2 
3 

13 
12 
11 

read  as  printed;  for 
100°+  or  280°+,  read 

50 

9.27  405 

66 

9.28  186 

69 

10.71  814 

9.99219 

2 

10 

co-function. 

51 

9.27471 

66 

9.28  254 

68 

10.71746 

9.99217 

2 

9 

52 

9.27537 

66 

9.28  323 

69 

10.71  677 

9.99214 

3 

8 

53 

9.27  602 

65 

9.28391 

68 

10.71609 

9.99212 

2 

7 

From  the  bottom: 

54 

9.27  668 

66 
66 

9.28  459 

68 
68 

10.71  541 

9.99209 

3 

2 

6 

For79°+or2590+, 

55 

56 
57 

9.27  734 
9.27  799 
9.27  864 

65 
65 

9.28  527 
9.28  595 
9.28  662 

68 
67 

10.71  473 
10.71405 
10.71338 

9.99  207 
9.99  204 
9.99202 

3 

2 

5 

4 
3 

read  as  printed;  for 
169°+or3490+,read 

58 

9.27  930 

66 

9.28  730 

68 

10.71  270 

9.99  200 

2 

2 

co-function. 

69 

9.27  995 

65 

9.28  798 

68 

10.71  202 

9.99  197 

3 

1 

60 

9.28  060 

65 

9.28  865 

67 

10.71  135 

9.99  195 

2 

0 

L  Cos 

d 

LCtn 

cd 

LTan 

LSin 

d 

' 

Prop.  Pts. 

79a  —  Logarithms  of  Trigonometric  Functions 


Ill]         11°  —  Logarithms  of  Trigonometric  Functions 


57 


/ 

LSin 

d 

L  Tan 

cd 

L  Ctn 

L  Cos 

d 

Prop.  Pts. 

0 

9.28  060 

9.28  865 

10.71  135 

9.99  195 

60 

1 

9.28  125 

65 

9.28  9335 

'68 

10.71  067 

9.99  192 

3 

59 

2 

9.28  190 

55 

9.29  000 

67 

10.71  000 

9.99  190 

2 

58 

68 

67 

66 

3 

4 

9.28  254 
9.28  319 

64 
•«5 
65 

%.29  067 
9.29  134 

67 
67 
67 

10.70933 
10.70866 

9.99  187 
9.99  185 

3 
2 
3 

57 
56 

2 
3 

13.6 
20.4 

13.4 
20.1 

13.2 
19.8 

5 

9.28  384 

9.29  201 

10.70799 

9.99  182 

55 

4 

27.2 

26.8 

26.4 

6 

9.28  448 

64 

9.29  268 

67 

10.70732 

9.99  180 

2 

54 

5 

34.0 

33.5 

33.0 

7 

9.28512 

64 

9.29  335 

67 

10.70  665 

9.99  177 

3 

53 

G 

40.8 

40.2 

39.6 

8 

9.28  577 

65 

9.29  402 

67 

10.70598 

9.99  175 

- 

52 

7 

47.6 

46.9 

46.2 

9 

9.28  641 

64 

9.29  468 

66 

10.70532 

9.99  172 

3 

51 

8 

54.4 

53.6 

52.8 

10 

9.28  705 

64 

9.29  535 

67 

10.70465 

9.99  170 

2 

50 

9 

61.2 

60.3 

59.4 

11 

9.28  769 

64 

9.29  601 

66 

10.70399 

9.99  167 

3 

49 

12 

9.28  833 

64 

9.29  668 

67 

10.70332 

9.99  165 

2 

48 

13 

9.28  896 

63 

9.29  734 

66 

10.70266 

9.99  162 

3 

47 

DO 

N 

OB 

14 

9.28  960 

64 

9.29  800 

66 

10.70200 

9.99  160 

2 

46 

2 

13.0 

12.8 

12.6 

15 

9.29  024 

64 

9.29  866 

66 

10.70  134 

9.99  157 

3 

45 

3 

19.5 

19.2 

18.9 

16 

9.29  087 

63 

9.29  932 

66 

10.70068 

9.99  155 

2 

44 

4 

26.0 

25.6 

25.2 

17 

9.29  150 

63 

9.29  998 

66 

10.70002 

9.99  152 

3 

43 

5 

32.5 

32.0 

31.5 

18 

9.29214 

64 

9.30  064 

66 

10.69936 

9.99  150 

2 

42 

G 

39.0 

38.4 

37.8 

19 

9.29  277 

63 

9.30  130 

66 

10.69  870 

9.99  147 

3 

41 

7 

45.5 

44.8 

44.1 

20 
21 

9.29  340 
9.29  403 

63 
63 

9.30  195 
9.30261 

65 
66 

10.69  805 
10.69739 

9.99  145 
9.99  142 

2 
3 

40 

39 

S 
9 

52.0 
58.5 

51.2 
57.6 

50.4 
56.7 

22 

9.29  466 

63 

9.30  326 

65 

10.69  674 

9.99  140 

2 

38 

23 

9.29  529 

63 

9.30391 

65 

10.69  609 

9.99  137 

3 

37 

62 

61 

60 

24 

9.29  591 

62 
63 

9.30  457 

66 
65 

10.69  543 

9.99  135 

2 

3 

36 

2 

12.4 

12.2 

12.0 

25 

9.29  654 

ftO 

9.30  522 

6" 

10.69478 

9.99  132 

35 

,3 

18.6 

18.3 

18.0 

26 

9.29  716 

021 

9.30  587 

o 

10.69413 

9.99  130 

2 

34 

4 

24.8 

24.4 

24.0 

27 

9.29  779 

63 

9.30  652 

65 
«- 

10.69  348 

9.99127 

3 

33 

5 

31.0 

30.5 

30.0 

28 

9.29  841 

62 

6n 

9.30717 

60 

«- 

10.69283 

9.99  124 

3 

32 

6 

37.2 

36.6 

36.0 

29 

9.29  903 

4 

63 

9.30  782 

o 
64 

10.69218 

9.99  122 

2 
3 

31 

7 

43.4 

42.7 

42.0 

30 

9.29  966 

9.30  846 

10.69  154 

9.99119 

30 

8 

49.6 

48.8 

48.0 

31 

9.30  028 

62 

9.30911 

65 

10.69089 

9.99117 

2 

29 

9 

55.8 

54.9 

54.0 

32 

9.30  090 

62 

9.30975 

64 

10.69  025 

9.99114 

3 

28 

33 

9.30  151 

61 

9.31  040 

65 

10.68900 

9.99112 

2 

27 

34 

9.30213 

62 

9.31  104 

64 

10.68896 

9.99  109 

3 

26 

59 

3 

2 

35 

9.30  275 

62 

9.31  168 

64 

10.68  832 

9.99  106 

3 

25 

2 

11.8 

0.6 

0.4 

36 

9.30  336 

61 

9.31  233 

65 

10.68767 

9.99  104 

2 

24 

3 

17.7 

0.9 

0.6 

37 

9.30  398 

62 

9.31  297 

64 

10.68703 

9.99  101 

3 

23 

4 

23.6 

1.2 

0.8 

38 

9.30459 

61 

9.31361 

64 

10.68  639 

9.99  099 

2 

22 

5 

29.5 

1.5 

1.0 

39 

9.30  521 

62 

9.31  425 

64 

10.68575 

9.99096 

3 

21 

6 

35.4 

1.8 

1.2 

40 

9.30  582 

61 

9.31  489 

64 

10.68511 

9.99  093 

3 

20 

7 

41.3 

2.1 

1.4 

41 

9.30  643 

61 

9.31  552 

63 

10.68448 

9.99091 

2 

19 

S 

47.2 

2.4 

1.6 

42 

9.30  704 

61 

9.31616 

64 

10.68384 

9.99  088 

3 

18 

9 

53.1 

2.7 

1.8 

43 

9.30  765 

61 

9.31  679 

63 

10.68321 

9.99  086 

2 

17 

44 

9.30  826 

61 

9.31  743 

64 

10.68257 

9.99  083 

3 

16 

45 

9.30  887 

61 

9.31  806 

63 

10.68  194 

9.99  080 

3 

15 

From  the  top: 

46 

9.30  947 

60 

9.31  870 

64 

10.68  130 

9.99078 

2 

14 

Forll0+orl91°+, 

47 
48 
49 

9.31  008 
9.31  068 
9.31  129 

61 
60 
61 

9.31  933 
9.31  996 
9.32  059 

63 
63 
63 

10.68067 
10.68  004 
10.67941 

9.99075 
9.99  072 
9.99  070 

3 
3 
2 

13 
12 
11 

read  as  printed  ;  for 
101°-|-or2810+,read 

50 

9.31  189 

60 

9.32  122 

63 

10.67  878 

9.99  067 

3 

10 

co-function. 

51 

9.31  250 

61 

9.32  185 

63 

10.67815 

9.99  064 

3 

9 

52 

9.31310 

60 

9.32  248 

63 

10.67752 

9.99062 

2 

8 

53 

9.31  370 

60 

9.32  311 

63 

10.67  689 

9.99  059 

3 

7 

From  the  bottom: 

54 

9.31  430 

60 
60 

9.32  373 

62 
63 

10.67  627 

9.99  056 

3 

2 

6 

For78°+or258°+? 

55 

56 
57 

9.31  490 
9.31  549 
9.31  609 

59 
60 

9.32  436 
9.32  498 
9.32  561 

62 
63 

10.67  564 
10.67502 
10.67439 

9.99  054 
9.99051 
9.99  048 

3 

3 

5 

4 
3 

read  as  printed;  for 
168°+  or  348°+,  read 

58 

9.31  669 

60 

9.32  623 

62 

10.67377 

9.99  046 

2 

2 

co-function. 

59 

9.31  728 

59 
60 

9.32  685 

62 
62 

10.67315 

9.99  043 

3 

3 

1 

60 

9.31  788 

9.32  747 

10.67253 

9.99  040 

a 

LCos 

d 

LCtn 

Cd 

LTan 

LSin 

d 

/ 

Prop.  Pts. 

78°  —  Logarithms  of  Trigonometric  Functions 


58 


12°  —  Logarithms  of  Trigonometric  Functions          [ill 


/ 

LSin 

d 

LTan 

cd 

LCtn 

LCos 

d 

Prop.  Pts. 

0 

9.31  788 

9.32  747 

10.67  253 

9.99  040 

60 

1 

9.31  847 

59 

9.32  810 

63 

10.67  190 

9.99038 

2 

59 

2 

9.31  907 

60 

9.32  872 

62 

10.67128 

9.99  035 

3 

58 

63 

62 

61 

3 
4 

9.31  966 
9.32  025 

59 
59 
59 

9.32  933 
9.32  995 

61 

62 
62 

10.67067 
10.67  005 

9.99  032 
9.99  030 

3 
2 
3 

57 
56 

2 
3 

12.6 
18.9 

12.4 
18.6 

12.2 
18.3 

5 

9.32  084 

9.33  057 

10.66943 

9.99  027 

55 

4 

25.2 

24.8 

24.4 

6 

9.32  143 

59 

9.33  119 

62 

10.66881 

9.99  024 

3 

54 

5 

31.5 

31.0 

30.5 

7 

9.32  202 

59 

9.33  180 

61 

10.66820 

9.99022 

2 

53 

6 

37.8 

37.2 

36.6 

8 

9.32  261 

59 

9.33  242 

62 

10.66758 

9.99019 

3 

52 

7 

44.1 

43.4 

42.7 

9 

9.32  319 

58 

9.33  303 

61 

10.66  697 

9.99016 

3 

51 

8 

50.4 

49.6 

48.8 

10 

9.32  378 

59 

9.33  365 

62 

10.66  635 

9.99013 

3 

50 

9 

56.7 

55.8 

54.9 

11 

9.32  437 

59 

9.33  426 

61 

10.66  574 

9.99011 

2 

49 

12 

9.32  495 

58 

9.33  487 

61 

10.66513 

9.99  008 

3 

48 

13 

9.32  553 

58 

9.33  548 

61 

10.66452 

9.99  005 

3 

47 

6U 

59 

58 

14 

9.32  612 

59 

9.33  609 

61 

10.66391 

9.99  002 

3 

46 

2 

12.0 

11.8 

11.6 

15 

9.32  670 

58 

9.33  670 

61 

10.66  330 

9.99  000 

2 

45 

3 

18.0 

17.7 

17.4 

16 

9.32  728 

58 

9.33  731 

61 

10.66269 

9.98997 

3 

44 

4 

24.0 

23.6 

23.2 

17 

9.32  786 

58 

9.33  792 

61 

10.66  208 

9.98994 

3 

43 

5 

30.0 

29.5 

29.0 

18 

9.32  844 

58 

9.33  853 

61 

10.66  147 

9.98991 

3 

42 

6 

36.0 

35.4 

34.8 

19 

9.32  902 

58 

9.33  913 

60 

10.66087 

9.98  989 

2 

41 

7 

42.0 

41.3 

40.6 

58 

61 

3 

g 

48.0 

47.2 

46.4 

20 

9.32  960 

9.33  974 

10.66  026 

9.98986 

40 

^•3  1 

21 

9.33  018 

58 

9.34  034 

60 

10.65  966 

9.98983 

3 

39 

54.0 

Oo.l 

52.2 

22 

9.33  075 

57 

9.34  095 

61 

10.65905 

9.98  980 

3 

38 

23 

9.33  133 

58 

9.34  155 

60 

10.65  845 

9.98978 

2 

37 

57      56 

24 

9.33  190 

57 

9.34215 

60 

10.65  785 

9.98975 

3 

36 

58 

61 

3 

2    11.4    11.2 

25 

9.33  248 

9.34  276 

10.65  724 

9.98  972 

35 

3    17.1    16.8 

26 

9.33  305 

57 

9.34  336 

60 

10.65664 

9.98969 

3 

34 

4    22.8    22.4 

27 

9.33  362 

57 

9.34  396 

60 

10.65  604 

9.98967 

33 

5    28.5    28.0 

28 

9.33  420 

58 

9.34  456 

60 

10.65  544 

9.98964 

32 

6    34.2    33  6 

29 

9.33  477 

57 
57 

9.34516 

60 
60 

10.65  484 

9,98961 

3 
3 

31 

7    39.9    39.2 

30 

9.33  534 

9.34  576 

10.65  424 

9.98958 

30 

8    45.6    44.8 

31 

9.33  591 

57 

9.34  635 

59 

10.65365 

9.98  955 

3 

29 

9    51.3    50.4 

32 

9.33  647 

56 

9.34  695 

60 

10.65305 

9.98953 

2 

28 

33 

9.33  704 

57 

9.34  755 

60 

10.65  245 

9.98950 

3 

27 

34 

9.33  761 

57 

9.34  814 

59 

10.65  186 

9.98  947 

3 

26 

55 

3 

2 

35 

9.33  818 

57 

9.34  874 

60 

10.65  126 

9.98944 

3 

25 

2 

11.0 

0.6 

0.4 

36 

9.33  874 

56 

9.34  933 

59 

10.65067 

9.98941 

3 

24 

3 

16.5 

0.9 

0.6 

37 

9.33  931 

57 

9.34  992 

59 

10.65008 

9.98938 

3 

23 

4 

22.0 

1.2 

0.8 

38 

9.33  987 

56 

9.35051 

59 

10.64  949 

9.98936 

2 

22 

5 

27.5 

1.5 

1.0 

39 

9.34  043 

56 

9.35  111 

60 

10.64  889 

9.98933 

3 

21 

6 

33.0 

1.8 

1.2 

40 

9.34  100 

57 

9.35  170 

59 

10.64  830 

9.98  930 

3 

20 

7 

38.5 

2.1 

1.4 

41 

9.34  156 

56 

9.35  229 

59 

10.64771 

9.98927 

3 

19 

8 

44.C 

2.4 

1.6 

42 

9.34212 

56 

9.35  288 

59 

10.64712 

9.98  924 

3 

18 

9 

49.5 

2.7 

1.8 

43 

9.34  268 

56 

9.35  347 

59 

10.64653 

9.98921 

3 

17 

44 

9.34  324 

56 

9.35  405 

58 

10.64595 

9.98919 

2 

16 

45 

9.34  380 

56 

9.35  464 

59 

10.64  536 

9.98916 

3 

15 

From  the  top: 

46 

9.34  436 

56 

9.35  523 

59 

10.64477 

9.98913 

3 

14 

Forl20+orl920+, 

47 
48 
49 

9.34491 
9.34  547 
9.34  602 

55 
56 
55 

9.35  581 
9.35  640 
9.35  698 

58 
59 

58 

10.64419 
10.64360 
10.64  302 

9.98910 
9.98907 
9.98904 

3 
3 
3 

13 
12 
11 

read  as  printed  ;  for 
1020+or2820+,read 

50 

9.34  658 

56 

9.35  757 

59 

10.64  243 

9.98901 

3 

10 

co-function. 

51 

9.34713 

55 

9.35  815 

58 

10.64  185 

9.98898 

3 

9 

52 

9.34  769 

56 

9.35  873 

58 

10.64127 

9.98896 

2 

8 

53 

9.34  824 

55 

9.35  931 

58 

10.64069 

9.98  893 

3 

7 

From  the  bottom: 

54 

9.34  879 

55 
55 

9.35  989 

58 
58 

10.64011 

9.98890 

3 
3 

6 

For77°-|-or2570+, 

55 

56 
57 

9.34  934 
9.34  989 
9.35  044 

55 
55 

9.36  047 
9.36  105 
9.36  163 

58 
58 

10.63  953 
10.63  895 
10.63  837 

9.98  887 
9.98  884 
9.98881 

3 
8 

5 

4 
3 

read  as  printed  ;  for 
167°+  or  347°+,  read 

58 

9.35  099 

55 

9.36221 

58 

10.63779 

9.98878 

3 

2 

co-function. 

59 

9.35  154 

55 

9.36  279 

58 

10.63  721 

9.98875 

3 

1 

60 

9.35  209 

55 

9.36  336 

57 

10.63  664 

9.98  872 

3 

0 

LCos 

d 

LCtn 

cd 

LTan 

LSin 

d 

' 

Prop.  Pts. 

77°  —  Logarithms  of  Trigonometric  Functions 


Ill]         13°  —  Logarithms  of  Trigonometric  Functions 


59 


1 

LSin 

d 

LTan 

cd 

L  Ctn 

LCos 

d 

Prop.  Pts. 

0 

9.35  209 

9.36  336 

10.63  664 

9.98  872 

60 

1 

9.35  263 

54 

9.36  394 

58 

10.63  606 

9.98869 

3 

59 

2 

9.35  318 

55 

9.36  452 

58 

10.63  548 

9.98  867 

2 

58 

58 

57 

56 

3 

9.35  373 

55 

9.36  509 

57 

10.63491 

9.98  864 

3 

57 

2 

11.6 

11.4 

11.2 

4 

9.35  427 

54 
54 

9.36  566 

57 
58 

10.63434 

9.98861 

3 

56 

3 

16.8 

5 

9.35  481 

9.36  624 

10.63  376 

9.98858 

55 

4 

23.2 

22'.8 

22.4 

6 

9.35  536 

55 

9.36  681 

57 

10.63319 

9.98  855 

3 

54 

5 

29.0 

28.5 

28.0 

7 

9.35  590 

54 

9.36  738 

57 

10.63  262 

9.98  852 

3 

53 

6 

34.8 

34.2 

33.6 

8 

9.35  644 

54 

9.36  795 

57 

10.63  205 

9.98849 

3 

52 

7 

10.6 

39.9 

39.2 

9 

9.35  698 

54 

9.36852 

57 

10.63  148 

9.98  846 

3 

51 

8 

16.4 

45.6 

44.8 

10 

9.35  752 

54 

9.36  909 

57 

10.63091 

9.98  843 

3 

50 

9 

52.2 

51.3 

50.4 

11 

9.35  806 

54 

9.36  966 

57 

10.63  034 

9.98840 

3 

49 

12 

9.35  860 

54 

9.37  023 

57 

10.62977 

9.98  837 

3 

48 

9.35914 

54 

9.37  080 

57 

10.62  920 

9.98  834 

3 

47 

55 

N 

BO 

14 

9.35  968 

54 

9.37  137 

57 

10.62863 

9.98831 

3 

46 

2 

11.0 

10.8 

10.6 

15 

9.36  022 

54 

9.37  193 

56 

10.62  807 

9.98828 

3 

45 

3 

16.5 

16.2 

15.9 

16 

9.36  075 

53 

9.37  250 

57 

10.62750 

9.98825 

3 

44 

4 

22.0 

21.6 

21.2 

17 

9.36  129 

54 

9.37  306 

56 

10.62694 

9.98822 

3 

43 

5 

27.5 

27.0 

26.5 

18 

9.36  182 

53 

9.37  363 

57 

10.62  637 

9.98819 

3 

42 

6 

33.0 

32.4 

31.8 

19 

9.36  236 

54 

9.37419 

56 

10.62581 

9.98816 

3 

41 

7 

38.5 

37.8 

37.1 

53 

57 

3 

8 

44.0 

43.2 

42.4 

20 

9.36  289 

9.37  476 

10.62524 

9.98  813 

40 

9 

48.6 

47.7 

21 

9.36  342 

53 

9.37  532 

56 

10.62468 

9.98810 

39 

22 

9.36  395 

53 

9.37  588 

56 

10.62412 

9.98807 

3 

38 

23 

9.36  449 

54 

9.37  644 

56 

10.62  356 

9.98  804 

3 

37 

52      51 

24 

9.36  502 

53 

9.37  700 

56 

10.62300 

9.98  801 

3 

36 

53 

56 

3 

i    10.4    10.2 

25 

9.36  555 

9.37  756 

10.62  244 

9.98798 

35 

3    15.6    15.3 

26 

9.36  608 

53 

9.37812 

56 

10.62  188 

9.98795 

34 

4    20.8    20.4 

27 

9.36  660 

52 

9.37  868 

56 

10.62  132 

9.98792 

33 

5    26.0    25.5 

28 

9.36713 

53 

9.37  924 

56 

10.62  076 

9.98789 

32 

6    31.2    30.6 

29 

9.36  766 

53 
53 

9.37  9SO 

56 
55 

10.62  020 

9.98786 

3 

31 

7    36.4    35.7 

30 

9.36  819 

9.38  035 

10.61  965 

9.98783 

30 

8   41.6    40.8 

31 

9.36  871 

52 

9.38091 

56 

10.61909 

9.98780 

3 

29 

9    46.8    45.9 

32 

9.36  924 

53 

9.38  147 

56 

10.61853 

9.98777 

3 

28 

33 

9.36  976 

52 

9.38  202 

55 

10.61798 

9.98774 

3 

27 

34 

9.37  028 

52 

9.38  257 

55 

10.61  743 

9.98771 

3 

26 

4 

3 

2 

35 

9.37  081 

53 

9.38313 

56 

10.61  687 

9.98768 

3 

25 

2 

0.8 

0.6 

0.4 

36 

9.37  133 

52 

9.38  368 

55 

10.61  632 

9.98765 

3 

24 

3 

1.2 

0.9 

0.6 

37 

9.37  185 

52 

9.38423 

55 

10.61577 

9.98762 

3 

23 

4 

1.6 

1.2 

0.8 

38 

9.37  237 

52 

9.38  479 

56 

10.61521 

9.98759 

3 

22 

5 

2.0 

1.5 

1.0 

39 

9.37  289 

52 

9.38  534 

55 

10.61  466 

9.98756 

3 

21 

6 

2.4 

1.8 

1.2 

40 

9.37  341 

52 

9.38  589 

55 

10.61411 

9.98  753 

3 

20 

7 

2.8 

2.1 

1.4 

41 

9.37  393 

52 

9.38  644 

55 

10.61356 

9.98750 

3 

19 

8 

3.2 

2.4 

1.6 

42 

9.37  445 

52 

9.38  699 

55 

10.61301 

9.98746 

4 

18 

9 

3.6 

2.7 

1.8 

43 

9.37  497 

52 

9.38  754 

55 

10.61  246 

9.98743 

3 

17 

44 

9.37  549 

52 

9.38  808 

54 

10.61  192 

9.98740 

3 

16 

45 

9.37  600. 

51 

9.38  863 

55 

10.61  137 

9.98737 

3 

15 

From  the  top: 

46 

9.37  652 

52 

9.38918 

55 

10.61082. 

9.98734 

3 

14 

F 

or  130+  or  1930+ 

47 
48 
49 

9.37  703 
9.37  755 
9.37  806 

51 
52 
51 

9.38972 
9.39  027 
9.39  082 

54 

55. 
55 

10.61  028 
10.60973 
10.60918 

9.98731 
9.98728 
9.98725 

3 
3 

13 
12 
11 

read  as  printed;  for 
1030+or2830+,read 

50 

9.37  858 

52 

9.39  136 

54 

10.60  864 

9.98722 

3 

10 

co-function. 

51 

9.37  909 

51 

9.39  190 

54 

10.60810 

9.98719 

3 

9 

52 

9.37  960 

51 

9.39  245 

55 

10.60755 

9.98715 

4 

8 

53 

9.38011 

51 

9.39  299 

54 

10.60701 

9.98712 

3 

7 

From  the  bottom: 

54 

9.38  062 

51 
51 

9.39  353 

54 
54 

10.60647 

9.98709 

3 

3 

6 

For  76°+  or  256°+, 

55 

56 

57 

9.38  113 
9.38  164 
9.38215 

51 

51 

9.39  407 
9.39  461 
9.39  515 

54 

54 

10.60593 
10.60539 
10.60485 

9.98706 
9.98  703 
9.98700 

3 

3 

5 

4 
3 

read  as  printed  ;  for 
166°+  or  346°+  read 

58 

9.38  266 

51 

9.39  569 

54 

10.60431 

9.98697 

3 

2 

co-function. 

59 

9.38317 

51 

9.39  623 

54 

10.60377 

9.98694 

3 

1 

60 

9.38  368 

51 

9.39  677 

54 

10.60323 

9.98  690 

4 

0 

LCos 

d 

LCtn 

cd 

L  Tan 

LSin 

"d 

' 

Prop.  Pts. 

76°  —  Logarithms  of  Trigonometric  Functions 


60 


14°  —  Logarithms  of  Trigonometric  Functions          [III 


' 

LSin 

d 

LTan 

cd 

L  Ctn 

L  Cos 

d 

Prop.  Pts. 

0 

9.38  368 

9.39  677 

10.60323 

9.98  690 

60 

1 

9.38  418 

50 

9.39731 

54 

10.60269 

9.98687 

3 

59 

2 

9.38  469 

51 

9.39  785 

54 

10.60215 

9.98684 

3 

58 

54 

53 

52 

3 
4 

9.38519 
9.38  570 

50 
51 
50 

9.39  838 
9.39  892 

53 
54 
53 

10.60  162 
10.60  108 

9.98681 
9.98678 

3 
3 
3 

57 
56 

2 
3 

10.8 
16.2 

10.6 
15.9 

10.4 
15.6 

5 

9.38  620 

9.39  945 

10.60055 

9.98  675 

55 

4 

21 

6 

21 

.2 

20.8 

6 

9.38  670 

50 

9.39  999 

54 

10.60001 

9.98671 

4 

54 

5 

27.0 

26.5 

26.0 

7 

9.38  721 

51 

9.40  052 

53 

10.59  948 

9.98  668 

3 

53 

6 

32.4 

31 

.8 

31.2 

8 

9.38771 

50 

9.40  106 

54 

10.59894 

9.98665 

3 

52 

7 

37.8 

37.1 

36.4 

9 

9.38  821 

50 

9.40  159 

53 

10.59  841 

9.98  662 

3 

51 

8 

43 

2 

42.4 

41.6 

10 

9.38  871 

50 

9.40  212 

53 

10.59  788 

9.98659 

3 

50 

9 

48.6 

47.7 

46.8 

11 

9.38  921 

50 

9.40  266 

54 

10.59734 

9.98  656 

3 

49 

12 

9.38  971 

50 

9.40  3191 

53 

10.59681 

9.98652 

4 

48 

13 

9.39  021 

50 

9.40  372 

53 

10.59  628 

9.98649 

3 

47 

51 

50 

49 

14 

9.39  071 

50 

9.40  425 

53 

10.59  575 

9.98  646 

3 

2 

10.2 

10.0 

9.8 

15 

9.39  121 

50 

9.40  478 

53 

10.59  522 

9."98l54T 

3 

45 

3 

15 

3 

15.0 

14.7 

16 

9.39  170 

49 

9.40  531 

53 

10.59469 

9.98640 

3 

44 

4 

204 

20.0 

19.6 

17 

9.39  220 

50 

9.40  684 

53 

10.59416 

9.98636 

4 

43 

5 

25 

5 

25.0 

24.5 

18 

9.39  270 

50 

9.40  636 

52 

10.59  364 

9.98633 

3 

42 

8 

30  6 

30.0 

29.4 

19 

9.39  319 

49 

9.40  689 

53 

10.59311 

9.98  630 

3 

41 

7 

35 

7 

35.0 

34.3 

20 

21 

9.39  369 
9.39418 

50 
49 

9.40  742 
9.40  795 

53 
53 

10.59  258 
10.59  205 

9.98627 
9.98623 

3 

4 

40 

39 

8 
9 

40.8 
45.9 

40.0 
45.0 

39.2 
44.1 

22 

9.39  467 

49 

9.40  847 

52 

10.59  153 

9.98620 

3 

38 

23 

9.39  517 

50 

9.40  900 

53 

10.59  100 

9.98617 

3 

37 

4& 

47 

24 

9.39  566 

49 

9.40  952 

52 
53 

10.59  048 

9.98614 

3 

4 

36 

2 

fi 

9.4 

25 

9.39  615 

9.41  005 

10.58  995 

9.98  610 

35 

3 

14.4 

14.1 

26 

9.39  604 

49 

9.41  057 

52 

10.58943 

9.98607 

34 

4 

19.2 

18.8 

27 

9.39713 

49 

9.41  109 

52 

10.58891 

9.98604 

3 

33 

5 

24.0 

23.5 

28 

9.39  762 

49 

9.41  161 

52 

10.58839 

9.98601 

3 

32 

6 

28.8 

28.2 

29 

9.39811 

49 
49 

9.41  214 

53 

52 

il0.58786 

9.98597 

4 
3 

31 

7 

33.6 

32.9 

30 

9.39  860 

9.41  266 

10.58734 

9.98594 

30 

8 

38.4 

37.6 

31 

9.39  909 

49 

9.41318 

52 

10.58682 

9.98591 

3 

29 

9 

43.2 

42.3 

32 

9.39  958 

49 

9.41  370 

52 

10.58630 

9.98588. 

3 

28 

33 

9.40  006 

48 

9.41  422 

52 

10.58578 

9.98584' 

4 

27 

34 

9.40  055 

49 

9.41  474 

52 

10.58526 

9.98581 

3 

26 

4 

3 

35 

9.40  103 

48 

9.41  626 

52 

10.58474 

9.98578 

3 

25 

2 

0.8 

0.6 

36 

9.40  152 

49 

9.41  678 

52 

10.58422 

9.98574 

4 

24 

3 

1.2 

0.9 

37 

9.40  200 

48 

9.41  629 

51 

10.58371 

9.98571 

3 

23 

4 

1 

.6 

1.2 

38 

9.40  249 

49 

9.41  681 

52 

10.58319 

9.98568 

3 

22 

5 

2.0 

1.5 

39 

9.40  297 

48 

9.41  733 

52 

10.58267 

9.98665 

3 

21 

6 

2.4 

1. 

S 

40 

9.40  346 

49 

9.41  784 

51 

10.58216 

9.98561 

4 

20 

7 

2.8 

2.1 

41 

9.40  394 

48 

9.41  836 

52 

10.58  164 

9.98558 

3 

19 

8 

3.2 

2.4 

42 

9.40  442 

48 

9.41  887 

51 

10.58113 

9.98555 

3 

18 

9 

3.6 

2.7 

43 

9.40  490 

48 

9.41  939 

52 

10.58061 

9.98551 

4 

17 

44 

9.40  638 

48 

9.41990 

51 

10.58010 

9.98548 

3 

16 

45 

9.40  686 

48 

9.42  041 

51 

10.57959 

9.98545 

3 

15 

From  the  top: 

46 

9.40  634 

48 

9.42  093 

52 

10.57  907 

9.98541 

4 

14 

Forl40+orl940+, 

47 
48 
49 

9.40  682 
9.40  730 
9.40  778 

48 
48 
48 

9.42  144 
9.42  195 
9.42  246 

51 
51 
51 

10.57856 
10.57805 
10.57  754 

9.98538 
9.98535 
9.98531 

3 

4 

13 
12 
11 

read  as  printed;  for 
104°-|-or284°+,read 

50 

9.40  825 

47 

9.42  297 

51 

10.57  703 

9.98  528 

3 

10 

co-function. 

51 

9.40  873 

48 

9.42  348 

51 

10.57  652 

9.98  525 

3 

9 

52 
53 

9.40  921 
9.40  968 

48 
47 

9.42  399 
9.42  450 

51 
51 

10.57601 
10.57550 

9.98521 
9.98518 

4 
3 

8 
7 

From  the  bottom: 

54 

9.41  016 

48 
47 

9.42  501 

51 

51 

10.57499 

9.98515 

3 
4 

6 

For750+or2550+, 

55 

56 
57 

9.41  063 
9.41  111 
9.41  158 

48 

47 

9.42  552 
9.42  603 
9.42  653 

51 

50 

10.57448 
10.57397 
10.57  347 

9.98511 
9.98508 
9.98505 

3 
8 

5 

4 
3 

read  as  printed;  for 
165°^or3450+,read 

58 

9.41  205 

47 

9.42  704 

51 

10.57  296 

9.98501 

4 

2 

co-function. 

59 

9.41  252 

47 

9.42  755 

51 

10.57  245 

9.98498 

3 

1 

60 

9.41  300 

48 

9.42  805 

50 

10.57  195 

9.98  494 

4 

0 

LCos 

d 

LCtn 

cd 

LTan 

LSin 

d 

' 

Prop.  Pts. 

75°  —  Logarithms  of  Trigonometric  Functions 


Ill]          15°  —  Logarithms  of  Trigonometric  Functions 


61 


/ 

LSin 

d 

LTan 

cd 

LCtn 

LCos 

d 

Prop.  Pts. 

0 

9.41  300 

9.42  805 

10.57  195 

9.98494 

60 

1 

9.41  347 

47 

9.42  856 

51 

10.57  144 

9.98491 

3 

59 

2 

9.41  394 

47 

9.42  906 

50 

10.57094 

9.98488 

3 

58 

51 

50 

49 

3 
4 

9.41  441 
9.41  488 

47 
47 

47 

9.42  957 
9.43  007 

51 
50 
50 

10.57  043 
10.56993 

9.98484 
9.98481 

4 
3 

4 

57 
56 

2 
3 

10.S 

15.: 

!    10.0 
!    15.0 

9.8 
14.7 

5 

9.41  535 

9.43  057 

10.56  943 

9.98477 

55 

4 

20.^ 

I    20.0 

19.6 

6 

9.41  582 

47 

9.43  108 

51 

10.56  892 

9.98474 

3 

54 

5 

25.1 

>    25.0 

24.5 

7 

9.41  628 

46 

9.43  158 

50 

10.56842 

9.98471 

3 

53 

G 

30.( 

>    30.0 

29.4 

8 

9.41  675 

47 

9.43  208 

50 

10.56792 

9.98467 

4 

52 

7 

35.1 

'    35.0 

34.3 

9 

9.41  722 

47 
dfi 

9.43  258 

50 
50 

10.56  742 

9.98464 

3 
.^ 

51 

S 

40.* 

\    40.0 

39.2 

10 

9.41  768 

^u 

9.43  308 

10.56  692 

9.98460 

50 

9 

45.J 

1    45.0 

44.1 

11 

9.41  815 

47 

9.43  358 

50 

10.56  642 

9.98457 

3 

49 

12 

9.41  861 

46 

9.43  408 

50 

10.56592 

9.98453 

4 

48 

13 

9.41  908 

47 

9.43  458 

50 

10.56542 

9.98450 

3 

47 

48 

4f 

46 

14 

9.41  954 

46 

9.43  508 

50 

10.56492 

9.98  *47 

3 

46 

2 

9.6 

.      9.4 

9.2 

15 

9.42  001 

47 

9.43  558 

50 

10.56442 

9.98443 

4 

45 

3 

14.4 

t    14.1 

13.8 

16 

9.42  047 

46 

9.43  607 

49 

10.56393 

9.98440 

3 

44 

4 

19.S 

,    18.8 

18.4 

17 

9.42  093 

46 

9.43  657 

50 

10.56343 

9.98436 

4 

43 

5 

24.C 

1    23.5 

23.0 

18 

9.42  140 

47 

9.43  707 

50 

10.56293 

9.98433 

3 

42 

G 

28.8 

\    28.2 

27.6 

19 

9.42  186 

46 

9.43  756 

49 

10.56  244 

9.98429 

4 

41 

7 

33.6 

•    32.9 

32.2 

20 
21 

9.42  232 
9.42  278 

46 
46 

9.43  806 
9.43  855 

50 
49 

10.56  194 
10.56  145 

9.98426 
9.98422 

3 

4 

40 

39 

S 
9 

38.4 
43.2 

:       37.6 

42.3 

36.8 
41.4 

22 

9.42  324 

46 

9.43  905 

50 

10.56095 

9.98419 

3 

38 

23 

9.42  370 

46 
46 

9.43  954 

49 
50 

10.56046 

9.98415 

4 

0 

37 

45 

44 

24 

9.42  416 

9.44  004 

10.55  996 

9.98412 

o 

36 

45 

49 

3 

2 

9.0 

j 

.8 

25 

9.42  461 

9.44  053 

10.55  947 

9.98409 

35 

3    ] 

3.5 

13 

9 

26 

9.42  507 

46 

9.44  102 

49 

10.55  898 

9.98405 

4 

34 

4    ] 

8.0 

17^6 

27 

9.42  553 

46 

9.44  151 

49 

10.55  849 

9.98402 

3 

33 

5    2 

2.5 

22.0 

28 

9.42  599 

46 

9.44  201 

50 

10.55799 

9.98398 

4 

32 

6    2 

7.0 

26.4 

29 

9.42  644 

45 
46 

9.44  250 

49 
49 

10.55  750 

9.98395 

3 
4 

31 

7    3 

1.5 

3o!s 

30 

9.42  690 

9.44  299 

10.55  701 

9.98391 

30 

8    3 

6.0 

35.2 

31 

9.42  735 

45 

9.44  348 

49 

10.55  652 

9.98  3SS 

3 

.29- 

9    4 

0.5 

39.6 

32 

9.42  781 

46 

9.44  397 

49 

10.55  603 

9.98384 

4 

28 

33 

9.42  826 

45 

9.44  446 

49 

10.55  554 

9.98381 

3 

27 

34 

9.42  872 

46 
45 

9.44  495 

49 
49 

10.55505 

9.98  377 

4 

4 

26 

4 

3 

35 

9.42  917 

9.44  544 

10.55  456 

9.98373 

25 

2 

0.8 

0.6 

36 

9.42  962 

45 

9.44  592 

48 

10.55408 

9.98370 

3 

24 

3 

1.2 

0.9 

37 

9.43  008 

46 

9.44  641 

49 

10.55359 

9.98366 

4 

2o 

4 

1.6 

1.2 

38 

9.43  053 

45 

9.44  690 

49 

10.55310 

9.98363 

3 

22 

5 

2.0 

1.5 

39 

9.43  098 

45 

9.44  738 

48 

10.55  262 

9.98359 

4 

21 

6 

2.4 

14 

J 

40 

9.43  143 

45 

9.44  787 

49 

10.55213 

9.98356 

3 

20 

7 

2.8 

2.1 

41 

9.43  188 

45 

9.44  836 

49 

10.55  164 

9.98352 

4 

19 

8 

3.2 

2.4 

42 

9.43  233 

45 

9.44  884 

48 

10.55116 

9.98349 

3 

18 

9 

3.6 

2.7 

43 

9.43  278 

45 

9.44  933 

49 

10.55  067 

9.98345 

4 

17 

44 

9.43  323 

45 

9.44  981 

48 

10.55019 

9.98342 

3 

16 

45 

9.43  367 

44 

9.45  029 

48 

10.54971 

9.98338 

4 

15 

From  the  top: 

46 

9.43  412 

45 

9.45  078 

49 

10.54922 

9.98334 

4 

14 

Forl5°->-orl950+, 

47 
48 
49 

9.43  457 
9.43  502 
9.43  546 

45 
45 
44 

9.45  126 
9.45  174 
9.45  222 

48 
48 
48 

10.54874 
10.54  826 
10.54778 

9.98331 
9.98327 
9.98324 

3 
4 
3 

13 
12 
11 

read  as  printed  ;  for 
1050+or2850+,read 

50 

9.43  591 

45 

9.45  271 

49 

10.54  729 

9.98320 

4 

10 

co-function. 

51 

9.43  635 

44 

9.45  319 

48 

10.54  681 

9.98317 

3 

9 

52 

9.43  680 

45 

9.45  367 

48 

10.54633 

9.98313 

4 

8 

53 

9.43  724 

44 

9.45415 

48 

10.54  585 

9.98309 

4 

7 

From  the  bottom: 

54 

9.43  769 

45 
44 

9.45  463 

48 
48 

10.54  537 

9.98306 

3 
4 

6 

For  74°+  or  254°+, 

55 

56 
57 

9.43  813 
9.43  857 
9.43  901 

44 
44 

9.45511 
9.45  559 
9.45  606 

48 
47 

10.54  489 
10.54441 
10.54394 

9.98302 
9.98299 
9.98295 

3 
4 

5 

4 
3 

read  as  printed;  for 
164°+  or  344°+,  read 

58 

9.43  946 

45 

9.45  654 

48 

10.54  346 

9.98291 

4 

2 

co-function. 

59 

9.43  990 

44 
44 

9.45  702 

48 
48 

10.54  298 

9.98288 

3 

4 

1 

60 

9.44  034 

9.45  750 

10.54  250 

9.98  284 

0 

LCos 

d 

L  Ctn 

cd 

LTan 

LSin 

d 

/ 

Prop.  Pts. 

74°  —  Logarithms  of  Trigonometric  Functions 


62 


16°  —  Logarithms  of  Trigonometric  Functions          [III 


1 

LSin 

d 

LTan 

cd 

LCtn 

L  Cos 

d 

Prop.  Pts. 

0 

9.44  034 

9.45  750 

10.54  250 

9.98  284 

60 

1 

9.44  078 

44 

9.45  797 

47 

10.54203 

9.98281 

3 

59 

2 

9.44  122 

44 

9.45  845 

48 

10.54  155 

9.98  277 

4 

58 

48 

47 

46 

3 

9.44  166 

44 

9.45  892 

47 

10.54  108 

9.98273 

4 

57 

2 

9.6 

9.4 

9  2 

4 

9.44  210 

44 
43 

9.45  940 

48 

47 

10.54  060 

9.98  270 

3 

4 

56 

3 

13^8 

5 

9.44  253 

9.45  987 

10.54013 

9.98  266 

55 

4 

19.2 

18.8 

18.4 

6 

9.44  297 

44 

9.46  035 

48 

10.53  965 

9.98262 

4 

54 

5 

24.C 

23.5 

23.0 

7 

9.44  341 

44 

9.46  082 

47 

10.53918 

9.98259 

3 

53 

6 

28.S 

28.2 

27.6 

8 

9.44  385 

44 

9.46  130 

48 

10.53  870 

9.98255 

4 

52 

7 

33.e 

32.9 

32.2 

9 

9.44  428 

43 

9.46  177 

47 

10.53  823 

9.98251 

4 

51 

8 

38.4 

37.6 

36.8 

10 

9.44  472 

44 

9.46  224 

47 

10.53  776 

9.98  248 

3 

50 

9 

43.2 

42.3 

41.4 

11 

9.44  516 

44 

9.46  271 

47 

10.53  729 

9.98  244 

4 

49 

12 

9.44  559 

43 

9.46  319 

48 

10.53  681 

9.98240 

4 

48 

13 

9.44  602 

43 

9.46  366 

47 

10.53  634 

9.98237 

3 

47 

45 

44 

43 

14 

9.44  646 

44 

9.46413 

47 

10.53  587 

9.98  233 

4 

46 

2 

9.C 

8.8 

8.6 

15 

9.44  689 

43 

9.46  460 

47 

10.53  540 

9.98  229 

4 

45 

3 

13.S 

13.2 

12.9 

16 

9.44  733 

44 

9.46  507 

47 

10.53  493 

9.98226 

3 

44 

4 

18.  C 

17.6 

17.2 

17 

9.44  776 

43 

9.46  554 

47 

10.53  446 

9.98222 

4 

43 

5 

22.£ 

22.0 

21.5 

18 

9.44  819 

43 

9.46  601 

47 

10.53399 

9.98218 

4 

42 

6 

27.C 

26.4 

25.8 

19 

9.44  862 

43 

9.46  648 

47 

10.53352 

9.98215 

3 

41 

7 

31.  £ 

30.8 

30.1 

43 

46 

4 

g 

36.  C 

35 

i 

34.4 

20 

9.44  905 

9.46  694 

10.53  306 

9.98211 

40 

40  c 

QO  ^ 

OQ    »T 

21 

9.44  948 

43 

9.46741 

47 

10.53  259 

9.98207 

4 

39 

OB 

OS.  / 

22 

9.44  992 

44 

9.46  788 

47 

10.53212 

9.98  204 

3 

38 

23 

9.45  035 

43 

9.46  835 

47 

10.53  165 

9.98200 

4 

37 

40 

41 

24 

9.45  077 

42 
43 

9.46  881 

46 
47 

10.53119 

9.98  196 

4 
4 

36 

2 

VM 

8.4 

25 

9.45  120 

9.46  928 

10.53  072 

9.98  192 

35 

3    1 

2.6 

12.3 

26 

9.45  163 

43 

9.46  975 

47 

10.53  025 

9.98189 

34 

4    ] 

6.8 

16.4 

27 

9.45  206 

43 

9.47  021 

46 

10.52979 

9.98  185 

4 

33 

5    2 

1.0 

20.5 

28 

9.45  249 

43 

9.47  068 

47 

10.52932 

9.98181 

32 

6    2 

5.2 

24.6 

29 

9.45  292 

43 

42 

9.47  114 

46 

46 

10.52  886 

9.98177 

4 
3 

31 

7    2 

9.4 

28.7 

30 

9.45  334 

9.47  160 

10.52  840 

9.98  174 

30 

8    3 

3.6 

32.8 

31 

9.45  377 

43 

9.47  207 

47 

10.52793 

9.98170 

4 

29 

9    5 

7.8 

36.9 

32 

9.45419 

42 

9.47  253 

46 

10.52747 

9.98166 

4 

28 

33 

9.45  462 

43 

9.47  299 

46 

10.52701 

9.98162 

4 

27 

34 

9.45  504 

42 

9.47  346 

47 

10.52654 

9.98  159 

3 

26 

4 

3 

35 

9.45  547 

43 

9.47  392 

46 

10.52  608 

9.98  155 

4 

25 

2 

0.8 

0.6 

36 

9.45  589 

42 

9.47  438 

46 

10.52562 

9.98  151 

4 

24 

3 

1.2 

0.9 

37 

9.45  632 

43 

9.47  484 

46 

10.52516 

9.98  147 

4 

23 

4 

1.6 

1.2 

38 

9.45  674 

42 

9.47  530 

46 

10.52470 

9.98  144 

3 

22 

5 

2.0 

1.5 

39 

9.45  716 

42 

9.47  576 

46 

10.52424 

9.98  140 

4 

21 

6 

2.4 

1.8 

40 

9.45  758 

42 

9.47  622 

46 

10.52  378 

9.98  136 

4 

20 

7 

2.8 

2.1 

41 

9.45  801 

43 

9.47  668 

46 

10.52332 

9.98  132 

4 

19 

8 

3.2 

2.4 

42 

9.45  843 

42 

9.47  714 

46 

10.52286 

9.98129 

3 

18 

9 

3.6 

2.7 

43 

9.45  885 

42 

9.47  760 

46 

10.52240 

9.98125 

4 

17 

44 

9.45  927 

42 

9.47  806 

46 

10.52  194 

9.98121 

4 

16 

45 

9.45  969 

42 

9.47  852 

46 

10.52  148 

9.98117 

4 

15 

From  the  top: 

46 

9.46011 

42 

9.47  897 

45 

10.52  103 

9.98113 

4 

14 

For  16°+  or  196°+, 

47 
48 
49 

9.46  053 
9.46  095 
9.46  136 

42 
42 
41 

9.47  943 
9.47  989 
9.48  035 

46 
46 
46 

10.52  057 
10.52011 
10.51965 

9.98110 
9.98106 
9.98  102 

3 

4 
4 

13 

12 
11 

read  as  printed  ;  for 
106°+  or  286°+,  read 

50 

9.46  178 

42 

9.48  080 

45 

10.51920 

9.98098 

4 

10 

co-function. 

51 

9.46  220 

42 

9.48  126 

46 

10.51874 

9.98094 

4 

9 

52 

9.46  262 

42 

9.48  171 

45 

10.51  829 

9.98090 

4 

8 

53 

9.46  303 

41 

9.48  217 

46 

10.51  783 

9.98087 

3 

7 

From  the  bottom: 

54 

9.46  345 

42 
41 

9.48  262 

45 

45 

10.51738 

9.98083 

4 

4 

6 

For  73°+  or  253°+ 

55 

56 

57 

9.46  386 
9.46  428 
9.46  469 

42 
41 

9.48  307 
9.48  353 
9.48  398 

46 
45 

10.51693 
10.51  647 
10.51  602 

9.98  07& 
9.98075 
9.98071 

4 

4 

5 

4 
3 

read  as  printed;  for 
163°+  or  343°+,  read 

58 

9.46511 

42 

9.48  443 

45 

10.51557 

9.98067 

4 

2 

co-function. 

59 

9.46  552 

41 

9.48  489 

46 

10.51511 

9.98063 

4 

1 

42 

45 

3 

60 

9.46  594 

9.48  534 

10.51  466 

9.98060 

0 

LCos 

d 

L  Ctn 

cd 

L  Tan 

LSin 

d 

' 

Prop.  Pts. 

—  Logarithms  of  Trigonometric  Functions 


Ill]          17°  —  Logarithms  of  Trigonometric  Functions 


63 


L  Sin 

d 

L  Tan 

cd 

L  Ctn 

L  Cos 

d 

Prop.  Pts. 

0 

9.46  594 

9.48  534 

10.51466 

9.98  060 

60 

1 

9.46  635 

41 

9.48  579 

45 

10.51421 

9.98  056 

4 

59 

2 

9.46  676 

41 

9.48  624 

45 

10.51  376 

9.98  052 

4 

58 

45 

44 

43 

3 

9.46  717 

41 

9.48  669 

45 

10.51331 

9.98  048 

4 

57 

n  f\ 

0     ( 

>        o  c 

4 

9.46  758 

41 
42 

9.48  714 

45 
45 

10.51  286 

9.98  044 

4 
4 

56 

3 

y.u 
13.5 

13.'. 

>      8.6 
I    12.9 

5 

9.46  800 

9.48  759 

10.51  241 

9.98  040 

55 

4 

18.0 

5    17.2 

6 

9.46841 

41 

9.48  804 

45 

10.51  196 

9.98036 

4 

54 

5 

22.5 

22.( 

)    21.5 

7 

9.46  882 

41 

9.48  849 

45 

10.51  151 

9.98  032 

4 

53 

6 

27.0 

26." 

I    25.8 

8 

9.46  923 

41 

9.48  894 

45 

10.51  106 

9.98  029 

3 

52 

7 

31 

5 

30.J 

\    30.1 

9 

9.46  964 

41 
41 

9.48  939 

45 
45 

10.51  061 

9.98  025 

4 

4 

51 

8 

36.0 

35.5 

J    34.4 

10 

9.47  005 

9.48  984 

10.51016 

9.98021 

50 

9 

40.5 

39.( 

5    38.7 

11 

9.47  045 

40 

9.49  029 

45 

10.50971 

9.98017 

4 

49 

12 

9.47  086 

41 

9.49  073 

44 

10.50927 

9.98013 

4 

48 

13 

9.47  127 

41 

9.49  118 

45 

10.50882 

9.98  009 

4 

47 

42 

41 

40 

14 

9.47  168 

41 

9.49  163 

45 

10.50837 

9.98  005 

4 

46 

2 

8.4 

8.; 

J      8.0 

15 

9.47  209 

41 

9.49  207 

44 

10.50  793 

9.98  001 

4 

45 

3 

12.6 

12.; 

\    12.0 

16 

9.47  249 

40 

9.49  252 

45 

10.50  748 

9.97  997 

4 

44 

4 

16.8 

16." 

I    16.0 

17 

9.47  290 

41 

9.49  296 

44 

10.50704 

9.97  993 

4 

43 

5 

21 

0 

20.i 

>    20.0 

18 

9.47  330 

40 

9.49  341 

45 

10.50659 

9.97  989 

4 

42 

6 

25.2 

24.( 

>    24.0 

19 

9.47  371 

41 

9.49  385 

44 

10.50615 

9.97  986 

3 

41 

7 

29.4 

28.' 

r   28.0 

20 
21 

9.47411 
9.47  452 

40 
41 

9.49  430 
9.49  474 

45 
44 

10.50  570 
10.50  526 

9.97  982 
9.97  978 

4 
4 

40 

39 

8 
9 

33.6 
37.8 

32.* 
36.< 

\    32.0 
)    36.0 

22 

9.47  492 

40 

9.49  519 

45 

10.50481 

9.97  974 

4 

38 

23 

9.47  533 

41 

9.49  563 

44 

10.50437 

9.97  970 

4 

37 

TO 

24 

9.47  573 

40 

9.49  607 

44 

10.50  393 

9.97  966 

4 

36 

O«7 

25 

9.47  613 

40 

9.49  652 

45 

10.50348 

9.97  962 

4 

35 

2 

7.8 

ni 

1.0 

1    H 

26 

9.47  654 

41 

9.49  696 

44 

10.50304 

9.97  958 

4 

34 

4 

,  i 
15.6 

l.O 

2  n 

27 

9.47  694 

40 

9.49  740 

44 

10.50  260 

9.97  954 

4 

33 

5 

19.5 

D«V 

2.5 

28 

9.47  734 

40 

9.49  784 

44 

10.50216 

9.97  950 

4 

32 

g 

23.4 

29 

9.47  774 

40 
40 

9.49  828 

44 
44 

10.50172 

9.97  946 

4 
4 

31 

7 

3.5 

30 

9.47  814 

9.49  872 

10.50  128 

9.97  942 

30 

8 

31.2 

4.0 

31 

9.47  854 

40 

9.49  916 

44 

10.50084 

9.97  938 

4 

29 

9 

35.1 

1.5 

32 

9.47  894 

40 

9.49  960 

44 

10.50  040 

9.97934 

4 

28 

33 

9.47  934 

40 

9.50  004 

44 

10.49  996 

9.97  930 

4 

27 

34 

9.47  974 

40 
40 

9.50  048 

44 
44 

10.49  952 

9.97  926 

4 
4 

26 

4 

3 

35 

9.48  014 

9.50  092 

10.49  908 

9.97  922 

25 

2 

0.8   C 

1.6 

36 

9.48  054 

40 

9.50  136 

44 

10.49  864 

9.97918 

4 

24 

3 

1 

.2    C 

37 

9.48  094 

40 

9.50  180 

44 

10.49820 

9.97914 

4 

23 

4 

1 

.6    1 

.2 

38 

9.48  133 

39 

9.50  223 

43 

10.49  777 

9.97910 

4 

22 

5 

2 

.0    1 

.5 

39 

9.48  173 

40 

9.50  267 

44 

10.49  733 

9.97906 

4 

21 

6 

2 

.4    1 

.8 

40 

9.48  213 

40 

9.50311 

44 

10.49689 

£.97  902 

4 

20 

7 

2 

.8    2 

.1 

41 

9.48  252 

39 

9.50  355 

44 

10.49  645 

9.97  898 

4 

19 

8 

3 

.2    2 

.4 

42 

9.48  292 

40 

9.50398 

43 

10.49  602 

9.97  894 

4 

18 

9 

3 

.6    2 

.7 

43 

9.48  332 

40 

9.50  442 

44 

10.49558 

9.97  890 

4 

17 

44 

9.48  371 

39 

9.50  485 

43 

10.49515 

9.97  886 

4 

16 

45 

9.48411 

40 

9.50  529 

44 

10.49471 

9.97  882 

4 

15 

From  the  top: 

46 

9.48  450 

39 

9.50572 

43 

10.49428 

9.97878 

4 

14 

For  17°+  or  197°+, 

47 

48 
49 

9.48  490 
9.48  529 
9.48  568 

40 
39 
39 

9.50  616 
9.50  659 
9.50  703 

44 
43 
44 

10.49  384 
10.49341 
10.49  297 

9.97  874 
9.97  870 
9.97  866 

4 
4 
4 

13 
12 
11 

read  as  print«d;  for 
107°+  or  287°+,  read 

50 

9.48  607 

39 

9.50  746 

43 

10.49  254 

9.97  861 

0 

10 

co-function. 

51 

9.48  647 

40 

9.50  789 

43 

10.49211 

9.97  857 

4 

9 

52 

9.48  686 

39 

9.50  833 

44 

10.49  167 

9.97  853 

4 

8 

53 

9.48  725 

39 

9.50  876 

43 

10.49  124 

9.97  849 

4 

7 

From  the  bottom: 

54 

9.48  764 

39 
39 

9.50919 

43 
43 

10.49  081 

9.97845 

4 
4 

6 

For  72°+  or  252°+ 

55 

56 
57 

9.48  803 
9.48  842 
9.48  881 

39 
39 

9.50  962 
9.51  005 
9.51  048 

43 
43 

10.49  038 
10.48995 
10.48  952 

9.97841 
9.97  837 
9.97  833 

4 

4 

5 

4 
3 

read  as  printed  ;  for 
1620+or342°-t-,read 

58 

9.48  920 

39 

9.51  092 

44 

10.48908 

9.97  829 

4 

2 

co-furction. 

59 

9.48  959 

39 
39 

9.51  135 

43 
43 

10.48  865 

9.97  825 

4 

1 

60 

9.48  998 

9.51  17S 

10.48822 

9.97821 

0 

LCos 

d 

L  Ctn 

c  d      L  Tan 

LSin 

d 

' 

Prop.  Pts. 

72°  —  Logarithms  of  Trigonometric  Functions 


64 


18°  —  Logarithms  of  Trigonometric  Functions          [III 


' 

LSin 

d 

LTan 

cd 

L  Ctn 

L  Cos 

d 

Prop.  Pts. 

0 

9.48  998 

9.51  178 

10.48  822 

9.97821 

60 

1 

9.49  037 

39 

9.51  221 

43 

10.48779 

9.97817 

4 

59 

2 

9.49  076 

39 

9.51  264 

43 

10.48736 

9.97812 

5 

58 

3 

9.49  115 

39 

9.51  306 

42 

10.48694 

9.97  808 

4 

57 

4 

9.49  153 

38 

9.51  349 

43 

10.48651 

9.97  804 

4 

56 

5 

9.49  192 

39 

9.51  392 

43 

10.48608 

9.97  800 

4 

55 

43 

42 

41 

6 

7 
8 
9 

9.49  231 
9.49  269 
9.49  308 
9.49  347 

39 
38 
39 
39 
38 

9.51  435 
9.51  478 
9.51  520 
9.51  563 

43 
43 
42 
43 
43 

10.48565 
10.48522 
10.48480 
10.48437 

9.97  796 
9.97792 
9.97  788 
9.97  784 

4 
4 
4 
4 
5 

54 
53 
52 
51 

2 
3 
4 
5 

8.6 
12.9 
17.2 
21.5 

8.4 
12.6 
16.8 
21.0 

8.2 
12.3 
16.4 
20.5 

10 

9.49  385 

9.51  606 

10.48394 

9.97  779 

50 

6 

25.8 

25.2 

24.6 

11 

9.49  424 

39 

9.51  648 

42 

10.48352 

9.97775 

4 

49- 

7 

30.1 

29.4 

28.7 

12 

9.49  462 

38 

9.51  691 

43 

10.48309 

9.97771 

4 

48 

8 

34.4 

33.6 

32.8 

13 

9.49  500 

38 

9.51  734 

43 

10.48266 

9.97  767 

4 

47 

9 

38.7 

37.8 

36.9 

14 

9.49  539 

39 

9.51  776 

42 

10.48224 

9.97763 

4 

46 

15 

9.49  577 

38 

9.51  819 

43 

10.48  181 

9.97759 

4 

45 

16 

9.49  615 

38 

9.51  861 

42 

10.48  139 

9.97  754 

5 

44 

oq 

00 

„— 

17 

9.49  654 

39 

9.51  903 

42 

10.48097 

9.97750 

4 

43 

O*7 

oo 

01 

18 

9.49  692 

38 

9.51  946 

43 

10.48054 

9.97746 

4 

42 

2 

7.8 

7.6 

7.4 

19 

9.49  730 

38 

9.51  988 

42 

10.48012 

9.97742 

4 

41 

3 

11.7 

11.4 

11.1 

20 

21 

22 
23 
24 

9.49  768 
9.49  806 
9.49  844 
9.49  882 
9.49  920 

38 
38 
38 
38 
38 
38 

9.52  031 
9.52  073 
9.52  115 
9.52  157 
9.52  200 

43 
42 
42 
42 
43 
42 

10.47969 
10.47927 
10.47  885 
10.47843 
10.47  800 

9.97738 
9.97  734 
9.97  729 
9.97  725 
9.97721 

4 
4 
5 
4 
4 
4 

40 

39 
38 
37 
36 

4 
5 
6 

7 
8 
9 

15.6 
19.5 
23.4 
27.3 
31.2 
35.1 

15.2 
19.0 
22.8 
26.6 
30.4 
34.2 

14.8 
18.5 
22.2 
25.9 
29.6 
33.3 

25 

9.49  958 

9.52  242 

10.47758 

9.97717 

35 

26 

9.49  996 

38 

9.52  284 

42 

10.47716 

9.97713 

4 

34 

27 

9.50  034 

38 

9.52  326 

42 

10.47674 

9.97  708 

5 

33 

28 

9.50  072 

38 

9.52  368 

42 

10.47  632 

9.97704 

4 

32 

36 

5 

4 

29 

9.50  110 

38 

9.52  410 

42 

10.47  590 

9.97700 

4 

31 

2 

7.2 

1.0 

0.8 

30 

9.50  148 

38 

9.52  452 

42 

10.47548 

9.97696 

4 

30 

3 

10.8 

1.5 

1.2 

31 

9.50  185 

37 

9.52  494 

42 

10.47  506 

9.97691 

5 

29 

4 

14.4 

2.0 

1.6 

32 

9.50  223 

38 

9.52  536 

42 

10.47464 

9.97  687 

4 

28 

5 

18.0 

2.5 

2.0 

33 

9.50  261 

38 

9.52  578 

42 

10.47422 

9.97  683 

4 

27 

6 

21.6 

3.0 

2.4 

34 

9.50  298 

37 

9.52  620 

42 

10.47  380 

9.97679 

4 

26 

7 

25.2 

3.5 

2.8 

35 

36 

9.50  336 
9.50  374 

38 
38 

9.52  661 
9.52  703 

41 
42 

10.47  339 
10.47  297 

9.97  674 
9.97  670 

5 
4 

25 

24 

8 
9 

32.4 

4.0 
4.5 

3.2 
3.6 

37 

9.50411 

37 

9.52  745 

42 

10.47  255 

9.97666 

4 

23 

38 

9.50  449 

38 

9.52  787 

42 

10.47213 

9.97662 

4 

22 

39 

9.50  486 

37 

9.52  829 

42 

10.47  171 

9.97657 

5 

21 

40 

9.50  523 

37 

9.52  870 

41 

10.47  130 

9.97  653 

4 

20 

41 

9.50561 

38 

9.52912 

42 

10.47  088 

9.97  649 

4 

19 

42 

9.50  598 

37 

9.52  953 

41 

10.47  047 

9.97  645 

4 

18 

From  the  top: 

43 

44 

9.50  635 
9.50  673 

37 
38 

9.52  995 
9.53  037 

42 
42 

10.47  005 
10.46  963 

9.97  640 
9.97  636 

5 
4 

17 
16 

For  18°+  or  198°+ 

45 

9.50710 

37 

9.53  078 

41 

10.46922 

9.97632 

4 

15 

read  as  printed;  for 

46 

9.50  747 

37 

9.53  120 

42 

10.46  880 

9.97628 

4 

14 

1080+or288°-1-,read 

47 

9.50  784 

37 

9.53  161 

41 

10.46  839 

9.97  623 

5 

13 

co-function. 

48 

9.50821 

37 

9.53  202 

41 

10.46798 

9.97619 

4 

12 

49 

9.50  858 

37 

9.53  244 

42 

10.46  756 

9.97615 

4 

11 

50 

9.50  896 

38 

9.53  285 

41 

10.46  715 

9.97610 

5 

10 

From  the  bottom: 

51 

9.50  933 

37 

9.53  327 

42 

10.46673 

9.97606 

4 

9 

For  71°+  or  251°+, 

52 
53 
54 

9.50  970 
9.51  007 
9.51  043 

37 
37 
36 

9.53  368 
9.53  409 
9.53  450 

41 
41 
41 

10.46632 
10.46591 
10.46550 

9.97  602 
9.97597 
9.97593 

4 
5 

4 

8 
7 
6 

read  as  printed;  for 
161°+  or  341°+,  read 

55 

9.51  080 

37 

9.53  492 

42 

10.46508 

9.97589 

4 

5 

co-function. 

56 

9.51  117 

37 

9.53  533 

41 

10.46467 

9.97584 

5 

4 

57 

9.51  154 

37 

9.53  574 

41 

10.46426 

9.97580 

4 

3 

58 

9.51  191 

37 

9.53615 

41 

10.46385 

9.97576 

4 

2 

59 

9.51  227 

36 

9.53  656 

41 

10.46344 

9.97571 

5 

1 

60 

9.51  264 

37 

9.53  697 

41 

10.46303 

9.97567 

4 

0 

LCos 

d 

LCtn 

cd 

LTan 

LSin 

d 

1 

Prop.  Pts. 

71°  —  Logarithms  of  Trigonometric  Functions 


Ill]          19°  —  Logarithms  of  Trigonometric  Functions 


65 


' 

LSin 

d 

L  Tan 

cd 

L  Ctn 

LCos 

d 

Prop.  Pts. 

0 

9.51  264 

9.53  697 

10.46  303 

9.97  567 

60 

1 

9.51  301 

37 

9.53  738 

41 

10.46  262 

9.97563 

4 

59 

2 

9.51  338 

37 

9.53  779 

41 

10.46  221 

9.97558 

5 

58 

3 

9.51  374 

36 

9.53  820 

41 

10.46  180 

9.97554 

4 

57 

4 

9.51411 

37 

9.53  861 

41 

10.46  139 

9.97550 

4 

56 

5 

9.51  447 

36 

9.53  902 

41 

10.46098 

9.97545 

5 

55 

41 

40 

39 

6 

9.51  484 

37 

9.53  943 

41 

10.46  057 

9.97541 

4 

54 

2 

8.2 

8.0 

7.8 

7 

9.51  520 

36 

3-r 

9.53  984 

41 

10.46016 

9.97536 

5 

53 

3 

12.0 

1L7 

8 
9 

9.51  557 
9.51  593 

7 
36 
36 

9.54  025 
9.54  065 

41 
40 
41 

10.45975 
10.45  935 

9.97532 
9.97528 

4 

4 

d 

52 
51 

4 
5 

ie!4 

20.5 

16.0 
20.0 

15.6 
19.5 

10 

9.51  629 

9.54  106 

10.45  894 

9.97523 

50 

6 

24.6 

24.0 

23.4 

11 

9.51  666 

37 

9.54  147 

41 

10.45  853 

9.97519 

4 

49 

7 

28.7 

28.0 

27.3 

12 

9.51  702 

36 

9.54  187 

40 

10.45813 

9.97515 

4 

48 

8 

32.8 

32.0 

31.2 

13 

9.51  738 

36 

9.54  228 

41 

10.45772 

9.97510 

5 

47 

9 

36.9 

36.0 

35.1 

14 

9.51  774 

36 

9.54  269 

41 

10.45731 

9.97506 

4 

46 

15 

9.51  811 

37 

9.54  309 

40 

10.45  691 

9.97501 

5 

45 

16 

9.51  847 

36 

9.54  350 

41 

10.45  650 

9.97497 

4 

44 

37 

36 

35 

17 

9.51  883 

36 

9.54  390 

40 

10.45610 

9.97492 

5 

43 

18 

9.51  919 

36 

9.54  431 

41 

10.45  569 

9.97488 

4 

42 

2 

7.4 

7.2 

7.0 

19 

9.51  955 

36 

9.54  471 

40 

10.45529 

9.97484 

•i 

41 

3 

11.1 

10.8 

10.5 

20 
21 
22 
23 
24 

9.51  991 
9.52  027 
9.52  063 
9.52  099 
9.52  135 

36 
36 
36 
36 
36 
36 

9.54  512 
9.54  552 
9.54  593 
9.54  633 
9.54  673 

41 
40 
41 
40 
40 
41 

10.45  488 
10.45448 
10.45  407 
10.45  367 
10.45  327 

9.97479 
9.97475 
9.97470 
9.97466 
9.97461 

B 
4 
5 
4 
5 
4 

40 

39 
38 
37 
36 

4 
5 
6 
7 
8 
9 

14.8 
18.5 
22.2 
25.9 
29.6 
33.3 

14.4 
18.0 
21.6 
25.2 
28.8 
32.4 

14.0 
17.5 
21.0 
24.5 
28.0 
31.5 

25 

9.52  171 

9.54  714 

10.45  286 

9.97457 

35 

26 

9.52  207 

36 

9.54  754 

40 

10.45  246 

9.97453 

4 

34 

27 

9.52  242 

35 

9.54  794 

40 

10.45  206 

9.97448 

5 

33 

28 

9.52  278 

36 

9.54  835 

41 

10.45  165 

9.97444 

4 

32 

34 

& 

4 

29 

9.52  314 

36 

9.54  875 

40 

10.45  125 

9.97439 

5 

31 

2 

6.8 

1.0 

0.8 

30 

9.52  350 

36 

9.54  915 

40 

10.45  085 

9.97435 

4 

30 

3 

10.2 

1.5 

1.2 

31 

9.52  385 

35 

9.54  955 

40 

10.45  045 

9.97430 

5 

29 

4 

13.6 

2.0 

1.6 

32 

9.52  421 

36 

9.54  995 

40 

10.45005 

9.97426 

4 

28 

5 

17.0 

2.5 

2.0 

33 

9.52  456 

35 

9.55  035 

40 

10.44965 

9.97421 

5 

27 

6 

20.4 

3.0 

2.4 

34 

9.52  492 

36 

9.55  075 

40 

10.44925 

9.97417 

4 

26 

7 

23.8 

3.5 

2.8 

35 

40 

5 

27.2 

4.0 

3.2 

35 

9.52  527 

9.55  115 

10.44885 

9.97412 

25 

Q  A 

36 

9.52  563 

36 

9.55  155 

40 

10.44  845 

9.97408 

4 

24 

30.  c 

4.5 

O.D 

37 

9.52  598 

35 

9.55  195 

40 

10.44  805 

9.97403 

5 

23 

38 

9.52  634 

36 

9.55  235 

40 

10.44765 

9.97399 

4 

22 

39 

9.52  669 

35 

9.55  275 

40 

10.44725 

9.97  394 

5 

21 

40 

9.52  705 

36 

9.55  315 

40 

10.44  685 

9.97  390 

4 

20 

41 

9.52  740 

35 

9.55  355 

40 

10.44645 

9.97385 

5 

19 

42 

9.52  775 

35 

9.55  395 

40 
on 

10.44  605 

9.97381 

4 

18 

From  the  top: 

43 
44 

9.52811 
9.52  846 

35 

9.55  434 
9.55  474 

W 
40 

10.44566 
10.44  526 

9.97376 
9.97372 

5 
4 

17 
16 

For  19°+  or  199°+ 

45 

9.52  881 

35 

9.55514 

40 

10.44  486 

9.97  367 

5 

15 

read  as  printed  ;  for 

46 

9.52  916 

35 

9.55  554 

40 

10.44446 

9.97363 

4 

14 

109°+or2890+,read 

47 

9.52  951 

35 

3C 

9.55  593 

39 

10.44407 

9.97358 

5 

13 

co-function. 

48 

9.52  986 

O 

9.55  633 

40 

10.44367 

9.97353 

5 

12 

49 
50 

9.53  021 
9.53  056 

35 
35 

9.55  673 
9.55  712 

40 
39 

10.44327 
10.44  288 

9.97349 
9.97  344 

4 
5 

11 
10 

From  the  bottom: 

51 

9.53  092 

36 

9.55  752 

40 

10.44248 

9.97  340 

4 

9 

For  70°+  or  250°+ 

52 
53 

54 

9.53  126 
9.53  161 
9.53  196 

34 
35 
35 

9.55  791 
9.55  831 
9.55  870 

39 
40 
39 

10.44  209 
10.44  169 
10.44  130 

9.97335 
9.97331 
9.97326 

5 
4 

8 
7 
6 

read  as  printed  ;  for 
1600+or3400+,read 

55 

9.53  231 

35 

9.55  910 

40 

10.44  090 

9.97322 

4 

5 

co-function. 

56 

9.53  266 

35 

9.55  949 

39 

10.44051 

9.97317 

5 

4 

57 

9.53  301 

35 

9.55  989 

40 

10.44011 

9.97312 

5 

3 

58 

9.53  336 

35 

9.56  028 

39 

10.43  972 

9.97308 

4 

2 

59 

9.53  370 

34 

9.56  067 

39 

10.43  933 

9.97303 

5 

1 

60 

9.53  405 

35 

9.56  107 

40 

10.43  893 

9.97  299 

4 

0 

LCos 

d 

LCtn 

cd 

LTan 

LSin 

d 

' 

Prop.  Pts. 

70°  —  Logarithms  of  Trigonometric  Functions 


66 


20°  —  Logarithms  of  Trigonometric  Functions          [III 


1 

LSin 

d 

LTan 

cd 

L  Ctn 

LCos 

d 

Prop.  Pts. 

0 

9.53  405 

9.56  107 

10.43  893 

9.97  299 

60 

1 

9.53  440 

35 

9.56  146 

39 

10.43  854 

9.97  294 

5 

59 

2 

9.53  475 

35 

9.56  185 

39 

10.43  815 

9.97289 

5 

58 

3 

9.53  509 

34 

9.56  224 

39 

10.43  776 

9.97  285 

4 

57 

4 

9.53  544 

35 

9.56  264 

40 

10.43  736 

9.97  280 

5 

56 

5 

9.53  578 

34 

9.56  303 

39 

10.43  697 

9.97  276 

4 

55 

40 

39 

38 

6 

9.53  613 

35 

9.56  342 

39 

10.43  658 

9.97271 

5 

54 

2 

8.0 

7.8 

7.6 

7 

9.53  647 

34 

9.56  381 

39 

10.43  619 

9.97  266 

53 

Q 

U7 

8 
9 

9.53  682 
9.53  716 

35 
34 
35 

9.56  420 
9.56  459 

39 
39 
39 

10.43  580 
10.43  541 

9.97262 
9.97257 

4 
5 
5 

52 
51 

O 

4 
5 

ie!o 

20.0 

.  / 

15.6 
19.5 

15!2 
19.0 

10 

9.53  751 

9.56  498 

10.43  502 

9.97252 

50 

6 

24.0 

23.4 

22.8 

11 

9.53  785 

34 

9.56  537 

39 

10.43463 

9.97  248 

4 

49 

7 

28.0 

27.3 

26.6 

12 

9.53  819 

34 

9.56  576 

39 

10.43  424 

9.97243 

5 

48 

8 

32.0 

31.2 

30.4 

13 

9.53  854 

35 

9.56615 

39 

10.43  385 

9.97238 

5 

47 

9 

36.0 

35.1 

34.2 

14 

9.53  888 

34 

9.56  654 

39 

10.43  346 

9.97  234 

4 

46 

15 

9.53  922 

34 

9.56  693 

39 

10.43  307 

9.97  229 

5 

45 

16 

9.53  957 

35 

9.56  732 

39 

10.43  268 

9.97224 

5 

44 

V7 

IK 

n. 

17 

9.53  991 

34 

9.56771 

39 

10.43  229 

9.97  220 

4 

43 

O  I 

Ow 

O4 

18 

9.54  025 

34 

9.56810 

39 

10.43  190 

9.97215 

5 

42 

2 

7.4 

7.0 

6.8 

19 

9.54  059 

34 

9.56  849 

39 

10.43  151 

9.97210 

5 

41 

3 

11.1 

10.5 

10.2 

20 

21 
22 
23 

24 

9.54  093 
9.54  127 
9.54  161 
9.54  195 
9.54  229 

34 
34 
34 
34 
34 
34 

9.56  887 
9.56  926 
9.56  965 
9.57  004 
9.57  042 

38 
39 
39 
39 
38 
39 

10.43  113 
10.43  074 
10.43035 
10.42996 
10.42958 

9.97  206 
9.97201 
9.97  196 
9.97  192 
9.97  187 

4 
5 
5 
4 
5 
5 

40 

39 
38 
37 
36 

4 
5 
6 
7 
8 
9 

14.8 
18.5 
22.2 
25.9 
29.6 
33.3 

14.0 
17.5 
21.0 
24.5 
28.0 
31.5 

13.6 
17.0 
20.4 
23.8 
27.2 
30.6 

25 

9.54  263 

9.57  081 

10.42919 

9.97  182 

35 

26 

9.54  297 

34 

9.57  120 

39 

10.42  880 

9.97  178 

4 

34 

27 

9.54  331 

34 

9.57  158 

38 

10.42  842 

9.97  173 

5 

33 

28 

9.54  365 

34 

9.57  197 

39 

10.42  803 

9.97  168 

5 

32 

98 

0 

4 

29 

9.54  399 

34 

9.57  235 

38 

10.42  765 

9.97  163 

5 

31 

2 

6.6 

1.0 

0.8 

30 

9.54  433 

34 

9.57  274 

39 

10.42726 

9.97  159 

4 

30 

3 

9.9 

1.5 

1.2 

31 

9.54  466 

33 

9.57  312 

38 

10.42  688 

9.97  154 

5 

29 

4 

13.2 

2.0 

1.6 

32 

9.54  500 

34 

9.57351 

39 

10.42  649 

9.97  149 

5 

28 

5 

16.5 

2.5 

2.0 

33 

9.54  534 

34 

9.57  389 

38 

10.42611 

9.97  145 

4 

27 

6 

19.8 

3.0 

2.4 

34 

9.54  567 

33 

9.57  428 

39 

10.42572 

9.97  140 

5 

26 

7 

23.1 

3.5 

2.8 

35 

36 

9.54  601 
9.54  635 

34 
34 

9.57  466 
9.57  504 

38 
38 

10.42534 
10.42496 

9.97  135 
9.97  130 

5 
5 

25 

24 

8 
9 

26.4 
29.7 

4.0 
4.5 

3.2 
3.6 

37 

9.54  668 

33 

9.57  543 

39 

10.42457 

9.97  126 

4 

23 

38 

9.54  702 

34 

9.57  581 

38 

10.42419 

9.97121 

5 

22 

39 

9.54  735 

33 

9.57  619 

38 

10.42  381 

9.97116 

5 

21 

40 

9.54  769 

34 

9.57  658 

39 

10.42  342 

9.97111 

5 

20 

41 

9.54  802 

33 

9.57  696 

38 

10.42  304 

9.97  107 

4 

19 

42 

9.54  836 

34 

9.57  734 

38 

OQ 

10.42  266 

9.97  102 

5 

18 

From  the  top: 

43 
44 

9.54  869 
9.54  903 

33 
34 

9.57  772 
9.57  810 

oo 
38 

10.42  228 
10.42  190 

9.97  097 
9.97  092 

5 

17 
16 

For  20°+  or  200°+, 

45 

9.54  936 

33 

9.57  849 

39 

10.42  151 

9.97  087 

5 

15 

read  as  printed;  for 

46 

9.54  969 

33 

9.57  887 

38 

10.42  113 

9.97  083 

4 

14 

1100+or2900+,read 

47 

9.55  003 

34 

9.57  925 

38 

oo 

10.42075 

9.97  078 

5 

13 

co-function. 

48 

9.55  036 

33 

9.57  963 

OO 

10.42  037 

9.97073 

5 

12 

49 
50 

9.55  069 
9.55  102 

33 
33 

9.58  001 
9.58  039 

38 
38 

10.41  999 
10.41  961 

9.97068 
9.97063 

5 
5 

11 
10 

From  the  bottom: 

51 

9.55  136 

34 

9.58077 

38 

10.41  923 

9.97059 

4 

9 

For690+or2490+, 

52 
53 
54 

9.55  169 
9.55  202 
9.55  235 

33 
33 
33 

9.58  115 
9.58  153 
9.58  191 

38 
38 
38 

10.41  885 
10.41  847 
10.41  809 

9.97  054 
9.97049 
9.97  044 

5 
5 

5 

8 
7 
6 

read  as  printed  ;  for 
1590+or3390+,read 

55 

9.55  268 

33 

9.58  229 

38 

10.41  771 

9.97039 

5 

5 

co-function. 

56 

9.55  301 

33 

9.58  267 

38 

10.41733 

9.97  035 

4 

4 

57 

9.55  334 

33 

9.58  304 

37 

10.41  696 

9.97  030 

5 

3 

58 

9.55  367 

33 

9.58  342 

38 

10.41  658 

9.97  025 

5 

2 

59 

9.55  400 

33 

9.58  380 

38 

10.41  620 

9.97  020 

5 

1 

60 

9.55  433 

33 

9.58418 

38 

10.41  582 

9.97015 

5 

0 

LCos 

d 

LCtn 

cd 

LTan 

LSin 

d 

' 

Prop.  Pts. 

69°  —  Logarithms  of  Trigonometric  Functions 


Ill]         21°  —  Logarithms  of  Trigonometric  Functions 


67 


' 

LSin 

d 

LTan 

cd 

LCtn 

LCos 

d 

Prop.  Pts. 

0 

9.55  433 

9.58  418 

10.41  582 

9.97015 

60 

1 

9.55  466 

33 

9.58  455 

37 

10.41  545 

9.97010 

5 

59 

2 

9.55  499 

33 

9.58  493 

38 

10.41  507 

9.97005 

5 

58 

3 

9.55  532 

33 

9.58531 

38 

10.41469 

9.97001 

4 

57 

4 

9.55  564 

32 
"33 

9.58  569 

38 
37 

10.41431 

9.96  996 

5 
5 

56 

5 

9.55  597 

Qq 

9.58  606 

10.41  394 

9.96991 

55 

38 

37 

36 

6 

9.55  630 

oo 
qq 

9.58644 

38 

10.41  356 

9.96  986 

5 

54 

2 

7.6 

7.4 

7.2 

7 

9.55  663 

OO 
oo 

9.58  681 

37 

10.41319 

9.96  981 

5 

53 

3    1 

11.1 

10.8 

8 

9.55  695 

Oil 

9.58719 

38 

10.41  281 

9.96976 

5 

52 

4.     1 

K   O 

9 

9.55  728 

33 
33 

9.58  757 

38 
37 

10.41243 

9.96971 

5 
5 

51 

rr       J.U..4 

5    19.0 

18.5 

is!o 

10 

9.55  761 

9.58  794 

10.41  206 

9.96966 

50 

6    22.8 

22.2 

21.6 

11 

9.55  793 

32 

qq 

9.58  832 

38 

10.41  168 

9.96  962 

4 

49 

7    26.6 

25.9 

25.2 

12 

9.55  826 

OO 

qo 

9.58  869 

37 

10.41  131 

9.96957 

5 

48 

8    30.4 

29.6 

28.8 

13 

9.55  858 

oJ 

qq 

9.58  907 

38 

10.41  093 

9.96  952 

5 

47 

9    34.2 

33.3 

32.4 

14 

9.55  891 

Oo 

9.58  944 

37 

10.41  056 

9.96  947 

5 

46 

15 

9.55  923 

32 

9.58  981 

37 

10.41  019 

9.96  942 

5 

45 

16 

9.55  956 

33 

qo 

9.59019 

38 

10.40981 

9.96937 

5 

44 

33         99         91 

17 

9.55  988 

M 

9.59  056 

37 

10.40944 

9.96  932 

5 

43 

M 

M 

VA 

18 

9.56  021 

33 

9.59  094 

38 

10.40906 

9.96  927 

5 

42 

2 

6.6 

6.4 

6.2 

19 

9.56  053 

32 

9.59  131 

37 

10.40869 

9.96922 

5 

41 

3 

9.9 

9.6 

9.3 

20 
21 
22 
23 
24 

9.56  085 
9.56  118 
9.56  150 
9.56  182 
9.56215 

32 

33 

32 
32 
33 
32 

9.59  168 
9.59  205 
9.59  243 
9.59  280 
9.59317 

37 
37 

38 
37 
37 
37 

10.40832 
10.40795 
10.40757 
10.40720 
10.40683 

9.96917 
9.96912 
9.96  907 
9.96  903 
9.96  898 

5 
5 
5 
4 
5 
5 

40 

39 
38 
37 
36 

4    13.2 
5    16.5 
6    19.8 
7    23.1 
8    26.4 
9    29.7 

12.8 
16.0 
19.2 
22.4 
25.6 
28.8 

12.4 
15.5 
18.6 
21.7 
24.8 
27.9 

25 

9.56  247 

9.59  354 

10.40  646 

9.96  893 

35 

26 

.9L5J5279 

32 

9.59  391 

37 

10.40609 

9.96  888 

5 

34 

27 

9.56311 

32 

9.59  429 

38 

10.40571 

9.96  883 

5 

33 

28 

9.56  343 

32 

9.59466 

37 

10.40534 

9.96  878 

5 

32 

6 

5 

4 

29 

9.56  375 

32 

9.59  503 

37 

10.40497 

9.96873 

5 

31 

2 

1.2 

1.0 

0.8 

30 

9.56  408 

33 

9.59  540 

37 

10.40460 

9.96  868 

5 

30 

3 

1.8 

1.5 

1.2 

31 

9.56  440 

32 

9.59  577 

37 

10.40423 

9.96863 

5 

29 

4 

2.4 

2.0 

1.6 

32 

9.56  472 

32 

9.59  614 

37 

10.40386 

9.96  858 

5 

28 

5 

3.0 

2.5 

2.0 

33 

9.56  504 

32 

9.59  651 

37 

10.40349 

9.96  853 

5 

27 

6 

3.6 

3.0 

2.4 

34 

9.56  536 

32 

9.59  688 

37 

10.40312 

9.96  848 

5 

26 

7 

4.2 

3.5 

2.8 

32 

37 

5 

4B 

4  n 

39 

35 

36 

9.56  568 
9.56  599 

31 

9.59  725 
9.59  762 

37 

10.40275 
10.40  238 

9.96843 
9.96  838 

5 

25 

24 

9 

.0 

5.4 

^t.w 
4.5 

,tj 

3.6 

37 

9.56631 

32 

9.59  799 

37 

10.40201 

9.96  833 

5 

23 

38 

9.56  663 

32 

9.59  835 

36 

10.40  165 

9.96828 

5 

22 

39 

9.56  695 

32 
32 

9.59  872 

37 
37 

10.40  128 

9.96823 

5 
5 

21 

40 

9.56  727 

9.59  909 

10.40091 

9.96818 

20 

41 

9.56  759 

32 

9.59  946 

37 

10.40054 

9.96813 

5 

19 

42 

9.56  790 

31 

qo 

9.59  983 

37 

10.40017 

9.96808 

5 

18 

From  the  top: 

43 
44 

9.56  822 
9.56  854 

OM 

32 

9.60019 
9.60  056 

36 
37 

10.39981 
10.39944 

9.96803 
9.96798 

5 
5 

17 
16 

For210+or2010+, 

45 

9.56  886 

32 

9.60  093 

37 

10.39907 

9.96793 

5 

15 

read  as  printed  ;  for 

46 

9.56917 

31 

9.60  130 

37 

10.39870 

9.96788 

5 

14 

Ill0+or2910+,read 

47 

9.56  949 

32 

q-i 

9.60  166 

36 

10.39  834 

9.96  783 

5 

13 

co-function. 

48 

9.56  980 

ol 

9.60  203 

37 

10.39  797 

9.96778 

5 

12 

49 

9.57  012 

32 

9.60  240 

37 

10.39  760 

9.96772 

6 

11 

50 

9.57  044 

32 

9.60  276 

36 

10.39724 

9.96767 

5 

10 

From  the  bottom: 

51 

9.57  075 

31 

9.60313 

37 

10.39  687 

9.96762 

5 

9 

For  68°+  or  248°+ 

52 
53 
54 

9.57  107 
9.57  138 
9.57  169 

31 

31 

9.60  349 
9.60  386 
9.60  422 

36 
37 
36 

10.39651 
10.39  614 
10.39  578 

9.96757 
9.96752 
9.96747 

5 

5 

5 

8 
7 
6 

read  as  printed;  for 
158°+  or  338°+,  read 

55 

9.57  201 

32 

9.60459 

37 

10.39541 

9.96742 

5 

5 

co-function. 

56 

9.57  232 

31 

9.60  495 

36 

10.39  505 

9.96737 

5 

4 

57 

9.57  264 

32 

9.60532 

37 

10.39468 

9.96732 

5 

3 

58 

9.57  295 

31 

9.60  568 

36 

10.39  432 

9.96727 

5 

2 

59 

9.57  326 

31 

9.60  605 

37 

10.39  395 

9.96722 

5 

1 

60 

9.57  358 

32 

9.60  641 

36 

10.39  359 

9.96717 

5 

0 

LCos 

d 

L  Ctn 

cd 

L  Tan 

LSin 

d 

1 

Prop.  Pts. 

68°  —  Logarithms  of  Trigonometric  Functions 


22°  —  Logarithms  of  Trigonometric  Functions          [III 


1 

LSin 

d 

LTan 

cd 

LCtn 

LCos 

d 

Prop.  Pte. 

0 

9.57  358 

9.60  641 

10.39359 

9.96717 

60 

1 

9.57  389 

31 

9.60  677 

36 

10.39323 

9.96711 

0 

59 

2 

9.57  420 

31 

9.60714 

37 

10.39286 

9.96  706 

5 

58 

3 

9.57451 

31 

9.60  750 

36 

10.39250 

9.96701 

5 

57 

4 

9.57  482 

31 

9.60  786 

36 

10.39214 

9.96696 

0 

56 

5 

9.57  514 

32 

9.60  823 

37 

10.39  177 

9.96  691 

0 

55 

37 

36 

35 

6 

7 
8 

9.57  545 
9.57  576 
9.57  607 

31 
31 
31 

9.60  859 
9.60  895 
9.60931 

36 
36 
36 

10.39  141 
10.39  105 
10.39  069 

9.96  686 
9.96681 
9.96676 

5 
6 

5 

54 
53 
52 

2 
3 

4 

7.4 
11.1 

Me 

7.2 
10.8 
14  4 

7.0 
10.5 
14  0 

9 

9.57  638 

31 
31 

9.60  967 

36 
37 

10.39  033 

9.96  670 

5 

51 

5 

.0 

18.5 

Xrt.rr 

18.0 

i^f\j 
17.5 

10 

9.57  669 

9.61  004 

10.38996 

9.96665 

50 

G 

22.2 

21.6 

21.0 

11 

9.57  700 

31 

9.61  040 

36 

10.38960 

9.96660 

0 

49 

7 

25.9 

25.2 

24.5 

12 

9.57  731 

31 

9.61  076 

36 

10.38924 

9.96655 

5 

48 

8 

29.6 

28.8 

28.0 

13 

9.57  762 

31 

9.61  112 

36 

10.38  888 

9.96  650 

5 

47 

9 

33.3 

32.4 

31.5 

14 

9.57  793 

31 

9.61  148- 

36 

10.38852 

9.96  646 

5 

46 

15 

9.57  824 

31 

9.61  184 

36 

10.38816 

9.96  640 

5 

45 

16 

9.57  855 

31 

9.61  220 

36 

10.38780 

9.96  634 

6 

44 

oo 

31 

^n 

17 

9.57  885 

30 

9.61  256 

36 

10.38  744 

9.96629 

5 

43 

38 

ol 

oO 

18 

9.57  916 

31 

9.61  292 

36 

10.38708 

9.96  624 

5 

42 

2 

6.4 

6.2 

6.0 

19 

9.57  947 

31 

9.61  328 

36 

10.38672 

9.96619 

5 

41 

3 

9.6 

9.3 

9.0 

20 

21 
22 
23 
24 

9.57  978 
9.58  008 
9.58  039 
9.58  070 
9.58  101 

31 

30 
31 
31 
31 
30 

9.61  364 
9.61  400 
9.61  436 
9.61472 
9.61  508 

36 
36 
36 
36 
36 
36 

10.38  636 
10.38600 
10.38  564 
10.38528 
10.38492 

9.96614 
9.96608 
9.96603 
9.96598 
9.96593 

0 

6 
5 
B 

5 
5 

40 

39 
38 
37 
36 

4 
5 
G 
7 
8 
9 

12.8 
16.0 
19.2 
22.4 
25.6 
28.8 

12.4 
15.5 
18.6 
21.7 
24.8 
27.9 

12.0 
15.0 
18.0 
21.0 
24.0 
27.0 

25 

9.58  13*1 

9.61  544 

10.38456 

9.96  588 

35 

26 

9.58  162 

31 

9.61  579 

35 

10.38421 

9.96  582 

6 

34 

27 

9.58  192 

30 

9.61  615 

36 

10.38385 

9.96  577 

5 

33 

28 

9.58  223 

31 

9.61  651 

36 

10.38349 

9.96572 

5 

32 

29 

6 

5 

29 

9.58  253 

30 

9.61  687 

36 

10.38313 

9.96567 

5 

31 

2 

5.8 

1.2 

1.0 

30 

9.58  284 

31 

9.61  722 

35 

10.38  278 

9.96  562 

5 

30 

3 

8.7 

1.8 

1.5 

31 

9.58314 

30 

9.61  758 

36 

10.38  242 

9.96556 

6 

29 

4 

11.6 

2.4 

2.0 

32 

9.58  345 

31 

9.61  794 

36 

10.38206 

9.96551 

5 

28 

5 

14.5 

3.0 

2.5 

33 

9.58  375 

30 

9.61  830 

36 

10.38  170 

9.96546 

5 

27 

6 

17.4 

3.6 

3.0 

34 

9.58  406 

31 

9.61  865 

35 

10.38  135 

9.96541 

5 

26 

7 

20.3 

4.2 

3.5 

30 

36 

6 

97  9 

4Q 

A  n 

35 

36 

9.58  436 
9.58  467 

31 

9.61  901 
9.61  936 

35 

10.38  099 
10.38  064 

9.96  535 
9.96530 

5 

25 

24 

9 

£t&*m 

26.1 

.O 

5.4 

^.v/ 

4.5 

37 

9.58  497 

30 

9.61  972 

36 

10.38028 

9.96525 

5 

23 

38 

9.58  527 

30 

9.62  008 

36 

10.37  992 

9.96520 

5 

22 

39 

9.58  557 

30 

9.62  043 

35 

10.37  957 

9.96514 

6 

21 

40 

9.58  588 

31 

9.62  079 

36 

10.37  921 

9.96  509 

5 

20 

41 

9.58618 

30 

9.62  114 

35 

10.37  886 

9.96504 

5 

19 

42 

9.58  648 

30 

9.62  150 

36 

3e 

10.37  850 

9.96498 

6 

18 

From  the  top: 

43 
44 

9.58  678 
9.58  709 

30 
31 

9.62  185 
9.62  221 

0 

36 

10.37815 
10.37779 

9.96  493 
9.96488 

5 

5 

17 
16 

For220+or202°+ 

45 

9.58  739 

30 

9.62  256 

35 

10.37  744 

9.96483 

5 

15 

read  as  printed;  for 

46 

9.58  769 

30 

9.62  292 

36 

10.37  708 

9.96477 

6 

14 

1120+or292°+,read 

47 

9.58  799 

30 

9.62  327 

35 

or 

10.37  673 

9.96472 

o 

13 

co-function. 

48 

9.58  829 

30 

9.62  362 

BO 

10.37638 

9.96467 

5 

12 

49 

9.58  859 

30 

9.62  398 

36 

10.37602 

9.96461 

6 

11 

50 

9.58  889 

30 

9.62  433 

35 

10.37  567 

9.96  456 

5 

10 

From  the  bottom: 

51 

9.58919 

30 

9.62  468 

35 

10.37532 

9.96451 

5 

9 

For  67°+  or  247°+ 

52 
53 
54 

9.58  949 
9.58  979 
9.59  009 

30 
30 
30 

9.62  504 
9.62  539 
9.62  574 

35 
35 

10.37496 
10.37461 
10.37426 

9.96445 
9.96440 
9.96435 

5 
5 

8 
7 
6 

read  as  printed;  for 
157°+  or  337°+,  read 

55 

9.59  039 

30 

9.62  609 

35 

10.37391 

9.96429 

6 

5 

co-function. 

56 

9.59  069 

30 

9.62  645 

36 

10.37355 

9.96424 

5 

4 

57 

9.59  098 

29 

9.62  680 

35 

10.37320 

9.96419 

5 

3 

58 

9.59  128 

30 

9.62715 

35 

10.37285 

9.96413 

6 

2 

59 

9.59  158 

30 

9.62  750 

35 

10.37250 

9.96408 

5 

1 

60 

9.59  188 

30 

9.62  785 

35 

10.37  215 

9.96403 

5 

0 

LCos 

d 

LCtn 

cd 

LTan 

LSin 

d 

' 

Prop.  Pts. 

67°  —  Logarithms  of  Trigonometric  Functions 


Ill]         23°  —  Logarithms  of  Trigonometric  Functions 


69 


/ 

LSin 

d 

LTan 

cd 

L  Ctn 

LCos 

d 

Prop.  Pts. 

0 

9.59  188 

9.62  785 

10.37  215 

9.96403 

60 

1 

9.59  218 

30 

9.62  820 

35 

10.37  180 

9.96397 

6 

59 

2 

9.59  247 

29 

9.62  855 

35 

10.37  145 

9.96392 

5 

58 

36 

35 

3 

9.59  277 

30 

9.62  890 

35 

OA 

10.37110 

9.96  387 

5 

57 

2 

7.2 

7.0 

4 

9.59  307 

30 

29 

9.62  926 

OO 

35 

10.37074 

9.96381 

5 

56 

3 

10.8 

10.5 

5 

9.59  336 

9.62  961 

10.37  039 

9.96  376 

55 

4 

14.4 

14.0 

6 

9.59  366 

30 

9.62  996 

35 

10.37004 

9.96370 

6 

54 

5 

18.0 

17.5 

7 

9.59  396 

30 

9.63  031 

35 

10.36969 

9.96365 

5 

53 

6 

21.6 

21.0 

8 

9.59  425 

29 

9.63  066 

35 

10.36  934 

9.96360 

5 

52 

7 

25.2 

24.5 

9 

9.59  455 

30 

9.63  101 

35 

10.36  899 

9.96  354 

6 

51 

8 

28.8 

28.0 

10 

9.59  484 

29 

9.63  135 

34 

10.36  865 

9.96  349 

5 

50 

9 

32.4 

31.5 

11 

9.59  514 

30 

9.63  170 

35 

10.36  830 

9.96343 

6 

49 

12 

9.59  543 

29 

9.63  205 

35 

10.36  795 

9.96338 

5 

48 

nA 

nt\ 

13 

9.59  573 

30 

9.63  240 

35 

10.36760 

9.96333 

5 

47 

M 

30 

14 

9.59  602 

29 

9.63  275 

35 

10.36725 

9.96327 

6 

46 

2 

6.8 

6.0 

J.5 

9.59  632 

30 

9.63  310 

35 

10.36  690 

9.96  322 

5 

45 

3 

10.2 

9.0 

16 

9.59  661 

29 

9.63  345 

35 

10.36  655 

9.96316 

6 

44 

4 

13.6 

12.0 

17 

18 

9.59  690 
9.59  720 

29 
30 

9.63  379 
9.63414 

34 
35 

10.36  621 
10.36  586 

9.96311 
9.96305 

5 
6 

43 
42 

5 
6 

17.0 
20.4 

15.0 
18.0 

19 

9.59  749 

29 

9.63  449 

35 

10.36551 

9.96300 

5 

41 

7 

23.8 

21.0 

29 

35 

6 

8 

27.2 

24.0 

20 

9.59  778 

9.63  484 

3»» 

10.36516 

9.96  294 

40 

9 

30.6 

27.0 

21 

9.59  808 

30 

9.63519 

a 

10.36481 

9.96  289 

39 

22 

9.59  837 

29 

9.63  553 

34 

10.36447 

9.96284 

5 

38 

23 

9.59  866 

29 

9.63  588 

35 

10.36412 

9.96  278 

6 

37 

29 

28 

24 

9.59  895 

29 
29 

9.63  623 

35 
34 

10.36  377 

9.96  273 

5 
6 

36 

2 

5.8 

5.6 

25 

9.59  924 

OA 

9.63  657 

oe 

10.36  343 

9.96  267 

35 

3 

8.7 

8.4 

26 

9.59  954 

oU 

9.63  692 

50 

10.36308 

9.96  262 

34 

4 

11.6 

11.2 

27 

9.59  983 

29 

OQ 

9.63  726 

34 

3K 

10.36  274 

9.96  256 

6 

33 

5 

14.5 

14.0 

28 

9.60012 

id 
nr\ 

9.63  761 

0 

3~ 

10.36  239 

9.96251 

32 

6 

17.4 

16.8 

29 

9.60  041 

fH 
29 

9.63  796 

D 

34 

10.36  204 

9.96  245 

5 

31 

7 

20.3 

19.6 

30 

9.60  070 

9.63  830 

10.36  170 

9.96  240 

30 

8 

23.2 

22.4 

31 

9.60  099 

29 

9.63  865 

35 

10.36  135 

9.96  234 

6 

29 

9 

26.1 

25.2 

32 

9.60  128 

29 

9.63  899 

34 

10.36  101 

9.96229 

5 

28 

33 

9.60  157 

29 

9.63  934 

35 

10.36066 

9.96223 

6 

27 

34 

9.60  186 

29 

9.63  968 

34 

10.36032 

9.96218 

5 

26 

6 

5 

35 

9.60  215 

29 

9.64  003 

35 

10.35  997 

9.96212 

6 

25 

2 

1.2 

1.0 

36 

9.60  244 

29 

9.64  037 

34 

10.35  963 

9.96207 

5 

24 

3 

1.8 

1.5 

37 

9.60  273 

29 

9.64  072 

35 

10.35928 

9.96201 

6 

23 

4 

2.4 

2.0 

38 

9.60  302 

29 

9.64  106 

34 

10.35  894 

9.96  196 

5 

22 

5 

3.0 

2.5 

39 

9.60  331 

29 

9.64  140 

34 

10.35  860 

9.96  190 

6 

21 

6 

3.6 

3.0 

40 

9.60  359 

28 

9.64  175 

35 

10.35  825 

9.96  185 

5 

20 

7 

4.2 

3.5 

41 

9.60  388 

29 

9.64  209 

34 

10.35  791 

9.96179 

6 

19 

4.8 

4.0 

42 

9.60417 

29 

9.64  243 

34 

10.35757 

9.96  174 

0 

18 

9 

5.4 

4.5 

43 

9.60  446 

29 

9.64  278 

35 

10.35722 

9.96  168 

C 

17 

44 

9.60  474 

28 

9.64  312 

34 

10.35  688 

9.96  162 

6 

16 

45 

9.60  503 

29 

9.64  346 

34 

10.35  654 

9.96  157 

5 

15 

From  the  top: 

46 

9.60  532 

29 

9.64  381 

35 

nt 

10.35619 

9.96  151 

6 

14 

For  23°+  or  203°+, 

47 
48 
49 

9.60561 
9.60  589 
9.60618 

29 
28 
29 

9.64415 
9.64  449 
9.64  483 

o4 

34 

34 

10.35  585 
10.35551 
10.35517 

9.96  146 
9.96  140 
9.96135 

5 
6 
5 

13 
12 
11 

read  as  printed;  for 
113°+  or  293°+,  read 

50 

9.60  646 

28 

9.64  517 

34 

10.35483 

9.96  129 

6 

10 

co-function. 

51 

9.60  675 

29 

9.64  552 

35 

10.35448 

9.96  123 

6 

9 

52 
53 

9.60  704 
9.60  732 

29 
28 

9.64  586 
9.64  620 

34 
34 

10.35414 
10.35  380 

9.96  118 
9.96112 

5 
6 

8 

7 

From  the  bottom: 

54 

9.60  761 

29 
28 

9.64  654 

34 
34 

10.35  346 

9.96  107 

5 

6 

6 

For  66°+  or  246°+, 

55 

56 
57 

9.60  789 
9.60  818 
9.60  846 

29 

28 

9.64  688 
9.64  722 
9.64  756 

34 
34 

10.35312 
10.35278 
10.35  244 

9.96  101 
9.96  095 
9.96  090 

6 
5 

5 

4 
3 

read  as  printed;  for 
156°+  or  336°+,  read 

58 

9.60  875 

29 

9.64  790 

34 

10.35210 

9.96084 

6 

2 

co-function. 

59 

9.60  903 

28 
28 

9.64  824 

34 
34 

10.35  176 

9.96079 

5 

6 

1 

60 

9.60  931 

9.64  858 

10.35  142 

9.96073 

0 

LCos 

d 

LCtn 

cd 

LTan 

LSin 

d 

/ 

Prop.  Pts. 

66°  —  Logarithms  of  Trigonometric  Functions 


70 


24°  —  Logarithms  of  Trigonometric  Functions          [111 


1 

LSin 

d 

LTan 

cd 

L  Ctn 

LCos 

d 

Prop.  Pts. 

0 

9.60  931 

9.64  858 

10.35  142 

9.96073 

60 

1 

9.60  960 

29 

9.64  892 

34 

10.35  108 

9.96  067 

6 

59 

2 

9.60  988 

28 

9.64  926 

34 

10.35  074 

9.96  062 

5 

58 

34 

33 

3 

9.61  016 

28 

Ofl 

9.64  960 

34 

O/l 

10.35  040 

9.96  056 

6 

57 

2 

6.8 

6.6 

4 

9.61  045 

A) 
28 

9.64  994 

o<± 

34 

10.35  006 

9.96  050 

6 
5 

56 

3 

10.2 

9.9 

5 

9.61  073 

9.65  028 

10.34  972 

9.96  045 

55 

4 

13.6 

13.2 

6 

9.61  101 

28 

9.65  062 

34 

10.34938 

9.96  039 

6 

54 

5 

17.0 

16.5 

7 

9.61  129 

28 

9.65  096 

34 

10.34904 

9.96  034 

5 

53 

6 

20.4 

19.8 

8 

9.61  15»' 

29 

9.65  130 

34 

10.34870 

9.96028 

6 

52 

7 

23.8 

23.1 

9 

9.61  186' 

28 

9.65  164 

34 

10.34836 

9.96022 

6 

51 

8 

27.2 

26.4 

10 

9.61  214 

28 

9.65  197 

33 

10.34803 

9.96017 

0 

50 

9 

30.6 

29.7 

11 

9.61  242 

28 

9.65  231 

34 

10.34769 

9.96011 

6 

49 

12 

9.61  270 

28 

9.65  265 

34 

10.34735 

9.96005 

6 

48 

on 

no 

13 

9.61  298 

28 

9.65  299 

34 

10.34701 

9.96000 

5 

47 

29 

28 

14 

9.61  326 

28 

9.65  333 

34 

10.34  667 

9.95  994 

6 

46 

2 

5.8 

5.6 

15 

9.61  354 

28 

9.65  366 

33 

10.34634 

9.95  988 

6 

45 

3 

8.7 

8.4 

16 

9.61  382 

28 

9.65  400 

34 

10.34600 

9.95  982 

6 

44 

4 

11.6 

11.2 

17 

9.61411 

29 

9.65  434 

34 

10.34566 

9.95977 

5 

43 

5 

14.5 

14.0 

18 

9.61  438 

27 

9.65  467 

33 

10.34533 

9.95971 

6 

42 

6 

17.4 

16.8 

19 

9.61  466 

28 

9.65  501 

34 

10.34499 

9.95  965 

6 

41 

7 

20.3 

19.6 

28 

34 

5 

3 

23.2 

22.4 

20 

9.61  494 

9.65  535 

10.34465 

9.95  960 

40 

9 

26.1 

25.2 

21 

9.61  522 

28 

9.65  568 

33 

10.34432 

9.95  954 

6 

39 

22 

9.61  550 

28 

9.65  602 

34 

10.34398 

9.95948 

6 

38 

23 

9.61  578 

28 

9.65  636 

34 

10.34364 

9.95942 

6 

37 

27 

6 

24 

9.61  606 

28 
28 

9.65  669 

33 
34 

10.34331 

9.95937 

5 
6 

36 

2 

5.4 

1.2 

25 

9.61  634 

9.65  703 

10.34  297 

9.95  931 

35 

3 

8.1 

1.8 

26 

9.61  662 

28 

9.65  736 

33 

10.34  264 

9.95925 

6 

34 

4 

io!s 

2!4 

27 

9.61  689 

27 

9.65  770 

34. 

10.34  230 

9.95  920 

5 

33 

5 

13.5 

3.0 

28 

9.61  717 

28 

9.65  803 

33 

10.34  197 

9.95914 

6 

32 

6 

16.2 

3.6 

29 

9.61  745 

28 
28 

9.65  837 

34 
33 

10.34  163 

9.95908 

6 
g 

31 

7 

18.9 

4.2 

30 

9.61  773 

9.65  870 

10.34  130 

9.95  902 

30 

8 

21.6 

4.8 

31 

9.61  800 

27 

9.65  904 

34 

10.34  096 

9.95  897 

5 

29 

9 

24.3 

5.4 

32 

9.61  828 

28 

9.65  937 

33 

10.34  063 

9.95  891 

6 

28 

33 

9.61  856 

28 

9.65  971 

34 

10.34029 

9.95  885 

6 

27 

34 

9.61  883 

27 

9.66004 

33 

10.33  996 

9.95  879 

6 

26 

5 

35 

9.61  911 

28 

9.66  038 

34 

10.33  962 

9.95  873 

6 

25 

2    1.0 

36 

9.61  939 

28 

9.66071 

33 

10.33929 

9.95  868 

5 

24 

3    1.5 

37 

9.61  966 

27 

9.66  104 

33 

10.33  896 

9.95  862 

6 

23 

4    2.0 

38 

9.61  994 

28 

9.66  138 

34 

10.33862 

9.95  856 

6 

22 

6    2.5 

39 

9.62  021 

27 

9.66  171 

33 

10.33  829 

9.95  850 

6 

21 

6    3.0 

40 

9.62  049 

28 

9.66  204 

33 

10.33  796 

9.95  844 

6 

20 

7    3.5 

8        A    l\ 

41 

9.62  076 

27 

9.66  238 

34 

10.33762 

9.95  839 

5 

19 

4.0 

42 

9.62  104 

28 

9.66  271 

33 

10.33  729 

9.95  833 

6 

18 

9    4.5 

43 

9.62  131 

27 

9.66  304 

33 

10.33  696 

9.95  827 

6 

17 

44 

9.62  159 

28 

9.66  337 

33 

10.33  663 

9.95  821 

6 

16 

45 

9.62  186 

27 

9.66371 

34 

10.33  629 

9.95  815 

6 

15 

From  the  top: 

46 

9.62  214 

28 

9.66  404 

33 

10.33596 

9.95810 

5 

14 

For  24°+  or  204°+, 

47 
48 
49 

9.62  241 
9.62  268 
9.62  296 

27 
27 
28 

9.66  437 
9.66  470 
9.66  503 

33 
33 
33 

10.33563 
10.33530 
10.33497 

9.95  804 
9.95798 
9.95792 

6 
6 
6 

13 
12 
11 

read  as  printed  ;  for 
114°+  or  294°+,  read 

50 

9.62  323 

27 

9.66  537 

34 

10.33463 

9.95  786 

6 

10 

co-function. 

51 

9.62  350 

27 

9.66  570 

33 

10.33430 

9.95780 

6 

9 

52 

9.62  377 

27 

9.66  603 

33 

10.33  397 

9.95775 

5 

8 

53 

9.62  405 

28 

9.66  636 

33 

10.33  364 

9.95  769 

0 

7 

From  the  bottom: 

54 

9.62  432 

27 
27 

9.66  669 

33 
33 

10.33331 

9.95763 

6 
6 

6 

For650+or245°+, 

55 

56 

57 

9.62  459 
9.62  486 
9.62  513 

27 

27 

9.66  702 
9.66735 
9.66  768 

33 
33 

10.33  298 
10.33265 
10.33232 

9.95757 
9.95751 
9.95745 

G 
f> 

5 

4 
3 

read  as  printed  ;  for 
155°+  or  335°+,  read 

58 

9.62  541 

28 

9.66801 

33 

10.33  199 

9.95739 

6 

2 

co-function. 

59 

9.62  568 

27 

9.66  834 

33 

10.33  166 

9.95  733 

6 

1 

60 

9.62  595 

27 

9.66  867 

33 

10.33  133 

9.95  728 

5 

0 

L  Cos 

d 

LCtn 

cd 

LTan 

LSin 

d 

/ 

Prop.  Pts. 

65°  —  Logarithms  of  Trigonometric  Functions 


Ill]          25°  —  Logarithms  of  Trigonometric  Functions 


71 


' 

LSin 

d 

LTan 

cd 

LCtn 

LCos 

d 

Prop.  Pts. 

0 

9.62  595 

9.66  867 

10.33  133 

9.95  728 

60 

1 

9.62  622 

27 

9.66  900 

33 

10.33  100 

9.95  722 

6 

59 

2 

9.62  649 

27 

9.66  933 

33 

10.33  067 

9.95716 

6 

58 

33 

32 

3 

9.62  676 

27 

9.66  966 

33 

00 

10.33  034 

9.95710 

6 

57 

2 

6.6 

6.4 

4 

9.62  703 

27 
27 

9.66  999 

oo 
33 

10.33  001 

9.95704 

6 

56 

3 

9.9 

9.6 

5 

9.62  730 

9.67  032 

10.32  968 

9.95  698 

55 

4 

13.2 

12.8 

6 

9.62  757 

27 

9.67  065 

33 

10.32  935 

9.95  692 

6 

54 

5 

16.5 

16.0 

7 

9.62  784 

27 

9.67  098 

33 

10.32  902 

9.95  686 

6 

53 

6 

19.8 

19.2 

8 

9.62811 

27 

9.67  131 

33 

10.32  869 

9.95  680 

6 

52 

7 

23.1 

22.4 

9 

9.62  838 

27 

9.67  163 

32 

10.32837 

9.95  674 

6 

51 

8 

26.4 

25.6 

10 

9.62  865 

27 

9.67  196 

33 

10.32  804 

9.95  668 

6 

50 

9 

29.7 

28.8 

11 

9.62  892 

27 

9.67  229 

33 

10.32771 

9.95  663 

5 

49 

12 

9.62  918 

26 

9.67  262 

33 

10.32738 

9.95  657 

6 

48 

fVT 

e\f» 

13 

9.62  945 

27 

9.67  295 

33 

10.32  705 

9.95651 

6 

47 

27 

26 

14 

9.62  972 

27 

9.67  327 

32 

10.32  673 

9.95  645 

6 

46 

2 

5.4 

5.2 

15 

9.62  999 

27 

9.67  360 

33 

10.32  640 

9.95639 

6 

45 

3 

8.1 

7.8 

16 

9.63  026 

27 

9.67  393 

33 

10.32  607 

9.95  633 

6 

44 

4 

10.8 

10.4 

17 

9.63  052 

26 

9.67  426 

33 

10.32  574 

9.95  627 

6 

43 

5 

13.5 

13.0 

18 

9.63  079 

27 

9.67  458 

32 

10.32  542 

9.95621 

6 

42 

6 

16.2 

15.6 

19 

9.63  106 

27 

9.67  491 

33 

10.32509 

9.95  615 

6 

41 

7 

18.9 

18.2 

27 

33 

6 

8 

21.6 

20.8 

20 

9.63  133 

9.67  524 

10.32  476 

9.95  609 

40 

g 

24.3 

23.4 

21 

9.63  159 

26 

9.67  556 

32 

10.32  444 

9.95  603 

6 

39 

22 

9.63  186 

27 

9.67  589 

33 

10.32411 

9.95  597 

6 

38 

23 

9.63213 

27 

9.67  622 

33 

10.32  378 

9.95591 

6 

37 

7 

6 

24 

9.63  239 

26 
27 

9.67  654 

32 
33 

10.32346 

9.95  585 

6 
6 

36 

2 

1.4 

1.2 

25 

9.63  266 

9.67  687 

oo 

10.32313 

9.95  579 

35 

3 

2.1 

1.8 

26 

9.63  292 

26 

9.67719 

62 

10.32  281 

9.95  573 

34 

4 

2.8 

2.4 

27 

9.63  319 

27 

9.67  752 

33 

00 

10.32  248 

9.95567 

6 

33 

5 

3.5 

3.0 

28 

9.63  345 

26 

9.67  785 

oo 

OO 

10.32215 

9.95561 

32 

6 

4.2 

3.6 

29 

9.63  372 

27 
26 

9.67  817 

62 
33 

10.32  183 

9.95  555 

6 
6 

31 

7 

4.9 

4.2 

30 

9.63  398 

9.67850 

10.32  150 

9.95  549 

30 

8 

5.6 

4.8 

31 

9.63  425 

27 

9.67  882 

32 

10.32  118 

9.95  543 

6 

29 

9 

6.3 

5.4 

32 

9.63  451 

26 

9.67915 

33 

10.32  085 

9.95537 

6 

28 

33 

9.63  478 

27 

9.67  947 

32 

10.32  053 

9.95531 

6 

27 

34 

9.63  504 

26 

9.67  980 

33 

10.32  020 

9.95525 

6 

26 

5 

35 

9.63  531 

27 

9.68  012 

32 

10.31  988 

9.95519 

6 

25 

2    1.0 

36 

9.63  557 

26 

9.68  044 

32 

10.31956 

9.95513 

6 

24 

3    1.5 

37 

9.63  583 

26 

9.68  077 

33 

10.31923 

9.95507 

6 

23 

4    2.0 

38 

9.63  610 

27 

9.68  109 

32 

10.31891 

9.95500 

7 

22 

5    2.5 

39 

9.63  636 

26 

9.68  142 

33 

10.31  858 

9.95494 

6 

21 

6    3.0 

40 

9.63  662 

26 

9.68  174 

32 

10.31  826 

9.95488 

6 

20 

7    3.5 

41 

9.63  689 

27 

9.68  206 

32 

10.31  794 

9.95482 

6 

19 

8    4.0 

9         A     K. 

42 

9.63  715 

26 

9.68  239 

33 

10.31761 

9.95476 

6 

18 

4.5 

43 

9.63  741 

26 

9.68271 

32 

10.31  729 

9.95470 

6 

17 

44 

9.63  767 

26 

9.68  303 

32 

10.31  697 

9.95464 

6 

16 

45 

9.63  794 

27 

9.68  336 

33 

10.31  664 

9.95458 

6 

15 

From  the  top: 

46 

9.63  820 

26 

9.68  368 

32 

Oo 

10.31  632 

9.95452 

6 

14 

For  25°+  or  205°+ 

47 
48 
49 

9.63  846 
9.63  872 
9.63  898 

26 
26 

9.68  400 
9.68432 
9.68  465 

O3f 

32 
33 

10.31  600 
10.31568 
10.31  535 

9.95446 
9.95440 
9.95  434 

6 
6 

13 
12 
11 

read  as  printed;  for 
115°+  or  295°+,  read 

50 

9.63  924 

26 

9.68  497 

32 

10.31  503 

9.95427 

7 

10 

co-function. 

51 

9.63  950 

26 

9.68  529 

32 

10.31471 

9.95421 

6 

9 

52 
53 

9.63  976 
9.64  002 

26 
26 

9.68561 
9.68  593 

32 
32 

10.31439 
10.31  407 

9.95415 
9.95409 

6 
6 

8 

7 

From  the  bottom: 

54 

9.64  028 

26 
26 

9.68  626 

33 
32 

10.31  374 

9.95403 

6 
6 

6 

For  64°+  or  244°+ 

55 
56 
57 

9.64  054 
9.64  080 
9.64  106 

26 
26 

9.68  658 
9.68  690 
9.68  722 

32 
32 

10.31  342 
10.31310 
10.31  278 

9.95  397 
9.95391 
9.95384 

6 

7 

5 

4 
3 

read  as  printed  ;  for 
154°+  or  334°+,  read 

58 

9.64  132 

26 

9.68  754 

32 

10.31  246 

9.95378 

6 

2 

co-function. 

59 

9.64  158 

26 
26 

9.68  786 

32 
32 

10.31214 

9.95  372 

6 

6 

1 

60 

9.64  184 

9.68818 

10.31  182 

9.95  366 

0 

LCos 

d 

L  Ctn 

cd 

L  Tan 

LSin 

d 

' 

Prop.  Pts. 

64°  —  Logarithms  of  Trigonometric  Functions 


72 


26°  —  Logarithms  of  Trigonometric  Functions          [III 


/ 

LSin 

d 

LTan 

cd 

LCtn 

LCos 

d 

Prop.  Pts. 

0 

9.64  184 

9.68818 

10.31  182 

9.95  366 

60 

1 

9.64  210 

26 

9.68  850 

32 

10.31  150 

9.95360 

6 

59 

2 

9.64  236 

26 

9.68882 

32 

10.31118 

9.95  354 

6 

58 

32 

31 

3 

9.64  262 

26 

nft 

9.68914 

32 

10.31086 

9.95  348 

G 

57 

2 

6.4 

6.2 

4 

9.64  288 

ao 

25 

9.68  946 

32 
32 

10.31  054 

9.95341 

6 

56 

3 

9.6 

9.3 

5 

9.64  313 

9.68  978 

10.31  022 

9.95  335 

55 

4 

12.8 

12.4 

6 

9.64  339 

26 

9.69  010 

32 

10.30990 

9.95329 

6 

54 

5 

16.0 

15.5 

7 

9.64  365 

26 

9.69  042 

32 

10.30958 

9.95323 

6 

53 

6 

19.2 

18.6 

8 

9.64-39T 

.  26 

9.69  074 

32 

10.30926 

9.95317 

6 

52 

7 

22.4 

21.7 

9 

9.64  417 

26 

9.69  106 

32 

10.30894 

9.95310 

7 

51 

8 

25.6 

24.8 

10 

9.64  442 

25 

9.69  138 

32 

10.30862 

9.95  304 

6 

50 

9 

28.8 

27.9 

11 

9.64  468 

26 

9.69  170 

32 

10.30830 

9.95  298 

6 

49 

12 

9.64  494 

26 

9.69  202 

32 

10.30798 

9.95  292 

6 

48 

rt/% 

OC 

13 

9.64  519 

25 

9.69  234 

32 

10.30766 

9.95286 

6 

47 

26 

25 

14 

9.64  545 

26 

9.69  266 

32 

10.30734 

9.95  279 

7 

46 

2 

5.2 

5.0 

15 

9.64  571 

26 

9.69  298 

32 

10.30  702 

9.95  273 

6 

45 

3 

7.8 

7.5 

16 

9.64  596 

25 

9.69  329 

31 

10.30671 

9.95  267 

6 

44 

4 

10.4 

10.0 

17 

9.64  622 

26 

9.69  361 

32 

10.30  639 

9.95  261 

6 

43 

6 

13.0 

12.5 

18 

9.64  647 

25 

9.69  393 

32 

10.30607 

9.95  254 

7 

42 

6 

15.6 

15.0 

19 

9.64  673 

26 

9.69  425 

32 

10.30575 

9.95  248 

6 

41 

7 

18.2 

17.5 

25 

32 

0 

8 

20.8 

20.0 

20 

9.64  698 

9.69  457 

10.30  543 

9.95  242 

40 

9 

23.4 

22.5 

21 

9.64  724 

26 

9.69  488 

31 

10.30512 

9.95  236 

6 

39 

22 

9.64  749 

25 

9.69  520 

32 

10.30480 

9.95  229 

7 

38 

23 

9.64  775 

26 

9.69  552 

32 

10.30448 

9.95  223 

6 

37 

24 

7 

24 

9.64  800 

25 
26 

9.69  584 

32 
31 

10.30416 

9.95217 

6 
6 

36 

2 

4.8 

1.4 

25 

9.64  826 

ne 

9.69  615 

10.30385 

9.95211 

35 

3 

7.2 

2.1 

26 

9.64  851 

80 

9.69  647 

32 

10.30353 

9.95  204 

34 

4 

9.6 

2.8 

27 

9.64  877 

26 

9.69  679 

32 

10.30321 

9.95  198 

6 

33 

5 

12.0 

3.5 

28 

9.64  902 

25 

O  K 

9.69  710 

31 

10.30290 

9.95  192 

6 

32 

6 

14.4 

4.2 

29 

9.64  927 

M 

26 

9.69  742 

32 
32 

10.30  258 

9.95  185 

Q 

31 

7 

16.8 

4.9 

30 

9.64  953 

9.69  774 

10.30  226 

9.95  179 

30 

8 

19.2 

5.6 

31 

9.64  978 

25 

9.69  805 

31 

10.30  195 

9.95  173 

6 

29 

9 

21.6 

6.3 

32 

9.65  003 

25 

9.69  837 

32 

10.30  163 

9.95  167 

6 

28 

33 

9.65  029 

26 

9.69  868 

31 

10.30132 

9.95  160 

7 

27 

34 

9.65  054 

25 

9.69  900 

32 

10.30  100 

9.95  154 

G 

26 

6 

35 

9.65  079 

25 

9.69  932 

32 

10.30  068 

9.95  148 

6 

25 

2    1.2 

36 

9.65  104 

25 

9.69  963 

31 

10.30037 

9.95  141 

7 

24 

3    1.8 

37 

9.65  130 

26 

9.69  995 

32 

10.30005 

9.95  135 

6 

23 

4    2.4 

38 

9.65  155 

25 

9.70  026 

31 

10.29  974 

9.95  129 

6 

22 

6    3.0 

39 

9.65  180 

25 

9.70  058 

32 

10.29  942 

9.95  122 

7 

21 

6    3.6 

40 

9.65  205 

25 

9.70  089 

31 

10.29911 

9.95116 

6 

20 

7    4.2 

8       A    Q 

41 

9.65  230 

25 

9.70  121 

32 

10.29  879 

9.95110 

6 

19 

4,o 

9K    A 

42 

9.65  255 

25 

9.70  152 

31 

10.29  848 

9.95  103 

7 

18 

5.4 

43 

9.65  281 

26 

9.70  184 

32 

10.29816 

9.95  097 

6 

17 

44 
45 

9.65  306 
9.65  331 

25 
25 

9.70  215 
9.70  247 

31 

32 

10.29  785 
10.29  753 

9.95  090 
9.95  084 

7 
6 

16 
15 

From  the  top: 

46 

9.65  356 

25 

9.70  278 

31 

10.29  722 

9.95  078 

6 

14 

For26°+or2060+, 

47 
48 
49 

9.65  381 
9.65  406 
9.65  431 

25 
25 
25 

9.70  309 
9.70  341 
9.70  372 

31 
32 
31 

10.29691 
10.29  659 
10.29  628 

9.95071 
9.95  065 
9.95  059 

7 
6 
6 

13 
12 
11 

read  as  printed;  for 
1160+or2960+,read 

50 

9.65  456 

25 

9.70  404 

32 

10.29  596 

9.95  052 

7 

10 

co-function. 

51 

9.65  481 

25 

9.70435 

31 

10.29  565 

9.95046 

6 

9 

52 
53 

9.65  506 
9.65531 

25 

25 

9.70  466 
9.70  498 

31 
32 

10.29  534 
10.29502 

9.95039 
9.95  033 

7 
G 

8 

7 

From  the  bottom: 

54 

9.65  556 

25 
24 

9.70  529 

31 
31 

10.29471 

9.95  027 

6 

7 

6 

For63°+or2430+, 

55 
56 
57 

9.65  580 
9.65  605 
9.65  630 

25 

25 

9.70  560 
9.70  592 
9.70  623 

32 
31 

10.29  440 
10.29408 
10.29  377 

9.95  020 
9.95014 
9.95007 

G 

7 

5 

4 
3 

read  as  printed;  for 
153°+  or  333°+,  read 

58 

9.65  655 

25 

9.70  654 

31 

10.29  346 

9.95001 

6 

2 

co-function. 

59 

9.65  680 

25 
25 

9.70  685 

31 
32 

10.29315 

9.94  995 

6 

7 

1 

60 

9.65  705 

9.70717 

10.29  283 

9.94  988 

0 

LCos 

d 

LCtn 

cd 

LTan 

LSin 

d 

/ 

Prop.  Pts. 

63°  —  Logarithms  of  Trigonometric  Functions 


Ill]         27°  —  Logarithms  of  Trigonometric  Functions 


73 


/ 

LSin 

d 

LTan 

cd 

L  Ctn 

L  Cos 

d 

Prop.  Pts. 

0 

9.65  705 

9.70717 

10.29  283 

9.94  988 

60 

1 

9.65  729 

24 

9.70  748 

31 

10.29252 

9.94  982 

6 

59 

a 

9.65  754 

25 

9.70  779 

31 

10.29221 

9.94975 

7 

58 

32 

31 

3 

9.65  779 

25 

9.70810 

31 

10.29  190 

9.94969 

6 

57 

2 

6.4 

6.2 

4 

9.65  804 

25 
24 

9.70841 

31 
32 

10.29  159 

9.94962 

7 
6 

56 

3 

9.6 

9.3 

5 

9.65  828 

9.70  873 

10.29  127 

9.94956 

55 

4 

12.8 

12.4 

6 

9.65  853 

25 

9.70  904 

31 

10.29  096 

9.94949 

7 

54 

5 

16.0 

15.5 

7 

9.65  878 

25 

9.70  935 

31 

10.29065 

9.94943 

6 

53 

6 

19.2 

18.6 

8 

9.65  902 

24 

9.70  966 

31 

10.29  034 

9.94936 

7 

52 

7 

22.4 

21.7 

9 

9.65  927 

25 

9.70  997 

31 

10.29  003 

9.94930 

6 

51 

8 

25.6 

24.8 

10 

9.65  952 

25 

9.71  028 

31 

10.28  972 

9.94923 

7 

50 

9 

28.8 

27.9 

11 

9.65  976 

24 

9.71  059 

31 

10.28941 

9.94917 

6 

49 

12 

9.66  001 

25 

9.71  090 

31 

10.28910 

9.94911 

6 

48 

f)f\             e\r* 

13 

9.66  025 

24 

9.71  121 

31 

10.28879 

9.94904 

7 

47 

30 

•B 

14 

9.66  050 

25 

9.71  153 

32 

10.28847 

9.94898 

6 

46 

2 

6.0 

5.0 

15 

9.66  075 

25 

9.71  184 

31 

10.28816 

9.94891 

7 

45 

3 

9.0 

7.5 

1C 

9.66  099 

24 

9.71215 

31 

10.28  785 

9.94885 

6 

44 

4 

12.0 

10.0 

17 

9.66  124 

25 

9.71  246 

31 

10.28754 

9.94878 

7 

43 

5 

15.0 

12.5 

18 

9.66  148 

24 

9.71277 

31 

10.28723 

9.94871 

7 

42 

6 

18.0 

15.0 

19 

9.66  173 

25 

9.71  308 

31 

10.28  692 

9.94  865 

6 

41 

7 

21.0 

17.5 

24 

31 

7 

8 

24.0 

20.0 

20 

9.66  197 

9.71  339 

10.28661 

9.94858 

40 

9 

27.0 

9.9.  .5 

21 

9.66  221 

24 

9.71  370 

31 

10.28630 

9.94  852 

6 

39 

22 

9.66  246 

25 

9.71  401 

31 

10.28  599 

9.94845 

7 

38 

23 

9.66  270 

24 

9.71  431 

30 

10.28569 

9.94839 

6 

37 

24 

23 

24 

9.66  295 

25 
24 

9.71  462 

31 
31 

10.28538 

9.94  832 

7 
6 

36 

2 

4.8 

4.6 

25 

9.66319 

9.71  493 

10.28507 

9.94  826 

35 

3 

7.2 

6.9 

26 

9.66  343 

24 

9.71  524 

31 

10.28476 

9.94819 

7 

34 

4 

9.6 

9.2 

27 

9.66  368 

25 

9.71  555 

31 

10.28445 

9.94813 

6 

33 

5 

12.0 

11.5 

28 

9.66  392 

24 

9.71  586 

31 

10.28414 

9.94  806 

7 

32 

6 

14.4 

13.8 

29 

9^6  416 

24 
25 

9.71  617 

31 
31 

10.28383 

9.94799 

7 

6 

31 

7 

16.8 

16.1 

30 

9.66  441 

9.71  648 

10.28  352 

9.94793 

30 

8 

19.2 

18.4 

31 

9.66  465 

24 

9.71  679 

31 

10.28321 

9.94786 

7 

29 

9 

21.6 

20.7 

32 

9.66  489 

24 

9.71  709 

30 

10.28291 

9.94780 

6 

28 

33 

9.66513 

24 

9.71  740 

31 

10.28260 

9.94773 

7 

27 

34 

9.66  537 

24 

9.71  771 

31 

10.28229 

9.94767 

6 

26 

7 

6 

35 

9.66  562 

25 

9.71  802 

31 

10.28  198 

9.94760 

7 

25 

2 

1.4 

1.2 

36 

9.66  586 

24 

9.71  833 

31 

10.28  167 

9.94753 

7 

24 

3 

2.1 

1.8 

37 

9.66  610 

24 

9.71  863 

30 

10.28  137 

9.94747 

6 

23 

4 

2.8 

2.4 

38 

9.66  634 

24 

9.71  894 

31 

10.28  106 

9.94  740 

7 

22 

6 

3.5 

3.0 

39 

9.66  65,8 

24 

9.71  925 

31 

10.28075 

9.94734 

6 

21 

6 

4.2 

3.6 

40 

9.66  682 

24 

9.71  955 

30 

10.28  045 

9.94727 

7 

20 

7 

4.9 

4.2 

41 

9.66  706 

24 

9.71  986 

31 

10.28014 

9.94  720 

7 

19 

J 

5.6 

4.8 

42 

9.66  731 

25 

9.72  017 

31 

10.27983 

9.94714 

6 

18 

9 

6.3 

5.4 

43 

9.66  755 

24 

9.72  048 

31 

10.27952 

9.94707 

7 

17 

44 

9.66  779 

24 

9.72  078 

30 

10.27922 

9.94700 

7 

16 

45 

9.66  803 

24 

9.72  109 

31 

10.27891 

9.94  694 

6 

15 

From  the  top: 

46 

9.66  827 

24 

9.72  140 

31 

nf\ 

10.27  860 

9.94  687 

7 

14 

For  27°+  or  207°+, 

47 
48 
49 

9.66  851 
9.66  875 
9.66  899 

24 
24 
24 

9.72  170 
9.72  201 
9.72  231 

OU 

31 
30 

10.27830 
10.27799 
10.27769 

9.94  680 
9.94  674 
9.94667 

7 
6 

7 

13 
12 
11 

read  as  printed;  for 
117°-*-  or  297°+  read 

50 

9.66  922 

23 

9.72  262 

31 

10.27  738 

9.94  660 

7 

10 

co-function. 

51 

9.66  946 

24 

9.72  293 

31 

10.27707 

9.94  654 

6 

9 

52 

9.66  970 

24 

9.72  323 

30 

10.27  677 

9.94  647 

7 

8 

53 

9.66  994 

24 

9.72  354 

31 

10.27  646 

9.94640 

7 

7 

From  the  bottom: 

54 

9.67  018 

24 
24 

9.72  384 

30 
31 

10.27616 

9.94  634 

6 
7 

6 

For  62°+  or  242°+ 

55 

56 
57 

9.67  042 
9.67  066 
9.67  090 

24 
24 

9.72  415 
9.72  445 
9.72  476 

30 
31 

10.27585 
10.27555 
10.27524 

9.94627 
9.94  620 
9.94614 

7 
6 

5 

4 
3 

read  as  printed;  for 
152°+  or  332°+,  read 

58 

9.67113 

23 

9.72  506 

30 

10.27494 

9.94  607 

7 

2 

co-function. 

59 

9.67  137 

24 

9.72  537 

31 

10.27  463 

9.94600 

7 

1 

60 

9.67161 

24 

9.72  567 

30 

10.27433 

9.94  593 

7 

0 

LCos 

d 

LCtn 

cd 

LTan 

LSin 

d 

i 

Prop.  Pts. 

62°  —  Logarithms  of  Trigonometric  Functions 


74 


28°  —  Logarithms  of  Trigonometric  Functions          [III 


1 

LSin 

d 

LTan 

cd 

LCtn 

L  Cos 

d 

Prop.  Pts. 

0 

9.67  161 

9.72  567 

10.27433 

9.94  593 

60 

1 

9.67  185 

24 

9.72  598 

31 

10.27402 

9.94  587 

6 

59 

2 

9.67  208 

23 

9.72  628 

30 

10.27372 

9.94  580 

7 

58 

31 

30 

3 

9.67  232 

24 

9.72  659 

31 

10.27341 

9.94573 

7 

57 

2 

6.2 

6.0 

4 

9.67  256 

24 
24 

9.72  689 

30 
31 

10.27311 

9.94567 

6 

7 

56 

3 

9.3 

9.0 

5 

9.67  280 

9.72  720 

10.27  280 

9.94560 

55 

4 

12.4 

12.0 

6 

9.67  303 

23 

9.72  750 

30 

10.27  250 

9.94553 

7 

54 

5 

15.5 

15.0 

7 

9.67  327 

24 

9.72  780 

30 

10.27  220 

9.94546 

7 

53 

6 

18.6 

18.0 

8 

9.67  350 

23 

9.72811 

31 

10.27  189 

9.94  540 

6 

52 

7 

21.7 

21.0 

9 

9.67  374 

24 

9.72  841 

30 

10.27  159 

9.94533 

7 

51 

8 

24.8 

24.0 

10 

9.67  398 

24 

9.72  872 

31 

10.27  128 

9.94  526 

7 

50 

9 

27.9 

27.0 

11 

9.67  421 

23 

9.72  902 

30 

10.27  098 

9.94519 

7 

49 

12 

9.67  445 

24 

9.72  932 

30 

10.27068 

9.94513 

6 

48 

f\r\             t~*  * 

13 

9.67  468 

23 

9.72  963 

31 

10.27037 

9.94  506 

7 

47 

M 

iM 

14 

9.67  492 

24 

9.72  993 

30 

10.27007 

9.94499 

7 

46 

2 

5.8 

4.8 

15 

9.67  SiS 

23 

9.73  023 

30 

10.26977 

9.94492 

7 

45 

3 

8.7 

7.2      - 

16 

9.67  539 

24 

9.73  054 

31 

10.26946 

9.94485 

7 

44 

4 

11.6 

9.6 

17 

9.67  562 

23 

9.73  084 

30 

10.26916 

9.94479 

6 

43 

5 

14.5 

12.0 

18 

9.67  586 

24 

9.73114 

30 

10.26886 

9.94472 

7 

42 

6 

•  ft  ~ 

17.4 

14.4 

19 

9.67  609 

23 

9.73  144 

30 

10.26  856 

9.94465 

7 

41 

7 

20.3 

16.8 

20 

9.67  633 

24 

9.73  175 

31 

10.26825 

9.94  458 

7 

40 

8 
9 

26.1 

91.fi 

21 

9.67  656 

23 

9.73  205 

30 

10.26795 

9.94451 

7 

39 

22 

9.67  680 

24 

9.73  235 

30 

10.26  765 

9.94  445 

6 

38 

23 

9.67  703 

23 

9.73  265 

30 

10.26  735 

9.94438 

7 

37 

23 

22 

24 

9.67  726 

23 
24 

9.73  295 

30 
31 

10.26  705 

9.94431 

7 
7 

36 

2 

4.6 

4.4 

25 

9.67  750 

9.73  326 

10.26  674 

9.94424 

35 

3 

6.9 

6.6 

26 

9.67  773 

23 

9.73  356 

30 

10.26  644 

9.94417 

7 

34 

4 

9.2 

8.8 

27 

9.67  796 

23 

9.73  386 

30 

10.26  614 

9.94410 

7 

33 

5 

11.5 

11.0 

28 

9.67  820 

24 

9.73  416 

30 

10.26  584 

9.94  404 

6 

32 

6 

13.8 

13.2 

29 

9.67  843 

23 
23 

9.73  446 

30 
30 

10.26  554 

9.94397 

7 

7 

31 

7 

16.1 

15.4 

30 

9.67  866 

9.73  476 

10.26  524 

9.94  390 

30 

8 

18.4 

17.6 

31 

9.67  890 

24 

9.73  507 

31 

10.26493 

9.94  383 

7 

29 

9 

20.7 

19.8 

32 

9.67913 

23 

9.73  537 

30 

10.26463 

9.94376 

7 

28 

33 

9.67  936 

23 

9.73  567 

30 

10.26433 

9.94  369 

7 

27 

34 

9.67  959 

23 

9.73  597 

30 

10.26403 

9.94362 

7 

26 

7 

6 

35 

9.67  982 

23 

9.73  627 

30 

10.26  373 

9.94  355 

7 

25 

2 

1.4 

1.2 

30 

9.68  006 

24 

9.73  657 

30 

10.26  343 

9.94  349 

6 

24 

3 

2.1 

1.8 

37 

9.68  029 

23 

9.73  687 

30 

10.26313 

9.94342 

7 

23 

4 

2.8 

2.4 

38 

9.68  052 

23 

9.73  747 

30 

10.26283 

9.94335 

7 

22 

5 

3.5 

3.0 

39 

9.68  075 

23 

9.73  747 

30 

10.26  253 

9.94328 

7 

21 

6 

4.2 

3.6 

40 

9.68  098 

23 

9.73  777 

30 

10.26  223 

9.94321 

7 

20 

7 

4.9 

K    A 

4.2 
40 

41 

9.68  121 

23 

9.73  807 

30 

10.26  193 

9.94314 

7 

19 

5.D 

.0 

42 

9.68  144 

23 

9.73  837 

30 

10.26  163 

9.94307 

7 

18 

9 

6.3 

S.4 

43 

9.68  167 

23 

9.73  867 

30 

10.26  133 

9.94300 

7 

17 

44 

9.68  190 

23 

9.73  897 

30 

10.26  103 

9.94  293 

7 

16 

45 

9.68  213 

23 

9.73  927 

30 

10.26073 

9.94  286 

7 

15 

From  the  top: 

46 

9.68  237 

24 

9.73  957 

30 

10.26043 

9.94279 

7 

14 

For  28°+  or  208°+ 

47 
48 
49 

9.68  260 
9.68  283 
9.68  3Q§ 

23 
23 
22 

9.73  987 
9.74  017 
9.74  047 

30 
30 
30 

10.26013 
10.25  983 
10.25  953 

9.94  273 
9.94  266 
9.94_259_ 

6 
7 
7, 

13 
12 
11 

read  as  printed;  for 
1180-1-  or  298°+  read 

50 

9.68  328 

23 

9.74  077 

30 

10.25  923 

9.94  252 

7 

10 

co-function. 

51 

9.68  351 

23 

9.74  107 

30 

10.25  893 

9.94245 

7 

9 

52 
53 

9.68  374 
9.68  397- 

123 
23 

9.74  137. 
9.74  166 

30 

29 

10.25  863 
10.25  834 

9.94238 
9.94231 

7 
7 

8 
7 

From  the  bottom: 

54 

9.68  420 

23 
23 

9.74  196 

30 
30 

10.25  804 

9.94224 

7 
7 

6 

For  610-1-  or  241°+, 

55 

56 
57 

9.68  443 
9.68  466 
9.68  489 

23 
23 

9.74  226 
9.74  256 
9.74  286 

30 

30 

10.25  774 
10.25744 
10.25714 

9.94217 
9.94210 
9.94203 

7 

7 

5 

4 
3 

read  as  printed;  for 
151°+  or  331°+  read 

58 

9.68512 

23 
oo 

9.74  316 

30 

10.25  684 

9.94  196 

7 

2 

co-function. 

59 

9.68  534 

yz 

9.74  345 

29 

10.25655 

9.94  189 

7 

1 

60 

9.68  557 

23 

9.74  375 

30 

10.25  625 

9.94  182 

7 

0 

LCos 

d 

LCtn 

cd 

L  Tan 

LSin 

d 

' 

Prop.  Pts. 

61°  —  Logarithms  of  Trigonometric  Functions 


Ill]         29°  —  Logarithms  of  Trigonometric  Functions 


75 


1 

LSin 

d 

LTan 

cd 

L  Ctn 

LCos 

d 

Prop.  Pts. 

0 

9.68  557 

9.74  375 

10.25  625 

9.94  182 

60 

1 

9.68  580 

23 

9.74  405 

30 

10.25595 

9.94  175 

7 

59 

. 

2 

9.68  603 

23 

9.74  435 

30 

10.25  565 

9.94  168 

7 

58 

-U 

3 

9.68  625 

22 

9.74  465 

30 

10.25  535 

9.94  161 

7 

57 

"^jO 

4 

9.68  648 

23 

9.74  494 

29 

10.25  506 

9.94  154 

7 

56 

IX 

23 

30 

7 

5 

9.68671 

9.74  524 

10.25  476 

9.94  147 

55 

30 

29 

6 

9.68  694 

23 

9.74  554 

30 

10.25  446 

9.94  140 

7 

54 

2 

Go 

K  Q 

7 

9.68716 

22 

9.74  583 

29 

10.25417 

9.94  133 

7 

53 

o 

•\j 
9n 

O.O 

c  7     - 

8 

9.68  739 

23 

9.74  613 

30 

10.25  387 

9.94  126 

7 

52 

o 
4 

•u 
12.0 

O.  1 

Uft 

9 

9.68  762 

23 

22 

9.74  643 

30 
30 

10.25  357 

9.94119 

7 

7 

51 

5 

isio 

.w 

14.5 

10 

9.68  784 

9.74  673 

10.25  327 

9.94112 

50 

6 

18.0 

17.4 

11 

9.68  807 

23 

9.74  702 

29 

10.25  298 

9.94  105 

7 

49 

7 

21.0 

20.3 

12 

9.68  829 

22 

9.74  732 

30 

10.25  268 

9.94098 

7 

48 

8 

24.0 

23.2 

13 

9.68  852 

23 

r>o 

9.74  762 

30 

10.25  238 

9.94  090 

8 

47 

9 

27.0 

26.1 

14 

9.68  875 

M 

9.74  791 

29 

10.25  209 

9.94083 

7 

46 

15 

9.68  897 

22 

9.74  821 

30 

10.25  179 

9.94  076 

7 

45 

16 

9.68  920 

23 

9.74851 

30 

10.25  149 

9.94  069 

7 

44 

oo 

99 

17 

9.68  942 

22 

9.74  880 

29 

10.25  120 

9.94  062 

7 

43 

BB 

10% 

18 

9.68  965 

23 

9.74  910 

30 

10.25  090 

9.94  055 

7 

42 

2 

4.6 

4.4 

19 

9.68  987 

22 

9.74  939 

29 

10.25  061 

9.94  048 

7 

41 

3 

6.9 

6.6 

20 

9.69  010 

23 

9.74  969 

30 

10.25031 

9.94  041 

7 

40 

4 

9.2 

nc 

8.8 
nr» 

21 
22 

9.69  032 
9.69  055 

22 
23 

9.74  998 
9.75  028 

29 
30 

10.25  002 
10.24  972 

9.94  034 
9.94  027 

7 
7 

39 
38 

6 

.0 

13.8 

1  />    ~t 

•U 

13.2 

•f    C      A 

23 

9.69  077 

22 

9.75  058 

30 

10.24  942 

9.94  020 

7 

37 

lO.l 

TO  4 

15.4 
17  fi 

24 

9.69  100 

23 

22 

9.75  087 

29 
30 

10.24913 

9.94012 

8 

7 

36 

9 

AO,*! 

20.7 

±.  4  ,\J 

19.8 

25 

9.69  122 

9.75  117 

10.24  883 

9.94005 

35 

26 

9.69  144 

22 

9.75  146 

29 

10.24  854 

9.93  998 

7 

34 

27 

9.69  167 

23 

9.75  176 

30 

10.24  824 

9.93  991 

7 

33 

28 

9.69  189 

22 

9.75  205 

29 

10.24  795 

9.93  984 

7 

32 

8 

7 

29 

9.69  212 

23 

9.75  235 

30 

10.24765 

9.93  977 

7 

31 

2 

1.6 

1.4 

30 

9.69  234 

22 

9.75  264 

29 

10.24  736 

9.93  970 

7 

30 

3 

2.4 

2.1 

31 

9.69  256 

22 

9.75  294 

30 

10.24706 

9.93  963 

7 

29 

4 

3.2 

2.8 

32 

9.69  279 

23 

9.75  323 

29 

10.24  677 

9.93  955 

8 

28 

5 

4.0 

3.5 

33 

9.69  301 

22 

9.75  353 

30 

10.24  647 

9.93  948 

7 

27 

6 

4.8 

4.2 

34 

9.69  323 

22 

9.75  382 

29 

10.24  618 

9.93  941 

7 

26 

7 

5.6 

4.9 

35 

36 

9.69  345 
9.69  368 

22 
23 

9.75411 
9.75  441 

29 
30 

10.24  589 
10.24559 

9.93  934 
9.93927 

7 

7 

25 

24 

8 
9 

6.4 
7.2 

5.6 
6.3 

37 

9.69  390 

22 

9.75  470 

29 

10.24530 

9.93  920 

7 

23 

38 

9.69412 

22 

9.75  500 

30 

10.24  500 

9.93912 

8 

22 

39 

9.69  434 

22 

9.75  529 

29 

10.24471 

9.93  905 

7 

21 

40 

9.69  456 

22 

9.75  558 

29 

10.24442 

9.93  898 

7 

20 

41 

9.69  479 

23 

9.75  588 

30 

10.24412 

9.93  891 

7 

19 

42 

9.69  501 

22 

9.75  617 

29 

10.24  383 

9.93  884 

7 

18 

From  the  top: 

43 

44 

9.69  523 
9.69  545 

22 
22 

9.75  647 
9.75  676 

30 
29 

10.24  353 
10.24324 

9.93  876 
9.93  869 

8 
7 

17 
16 

For290+or2090+, 

45 

9.69  567 

22 

9.75  705 

29 

10.24  295 

9.93  862 

7 

15 

read  as  printed;  for 

46 

9.69  589 

22 

9.75  735 

30 

10.24  265 

9.93  855 

7 

14 

119°+  or  2990-1-,  read 

47 

9.69  611 

22 

9.75  764 

29 

10.24236 

9.93  847 

8 

13 

co-function. 

48 

9.69  633 

22 

9.75  793 

29 

10.24207 

9.93  840 

7 

12 

49 

9.69  655 

22 

9.75  822 

29 

10.24178 

9.93  833 

7 

11 

50 

9.69  677 

22 

9.75  852 

30 

10.24  148 

9.93  826 

7 

10 

From  the  bottom: 

51 

9.69  699 

22 

9.75  881 

29 

10.24119 

9.93819 

7 

9 

For60°+or2400+, 

52 
53 

54 

9.69  721 
9.69  743 
9.69  765 

22 
22 
22 

9.75  910 
9.75  939 
9.75  969 

29 
29 
30 

10.24090 
10.24061 
10.24031 

9.93811 
9.93  804 
9.93797 

8 
7 

7 

8 
7 
6 

read  as  printed;  for 
150°+  or  330°+,  read 

55 

9.69  787 

22 

9.75  998 

29 

10.24  002 

9.93  789 

S 

5 

co-function. 

56 

9.69  809 

22 

9.76  027 

29 

10.23  973 

9.93782 

7 

4 

57 

9.69  831 

22 

9.76  056 

29 

10.23  944 

9.93775 

7 

3 

58 

9.69  853 

22 

9.76  086 

30 

10.23914 

9.93  768 

7 

o 

59 

9.69  875 

22 

9.76  115 

29 

10.23  885 

9.93  760 

S 

1 

60 

9.69  897 

22 

9.76  144 

29 

10.23  856 

9.93  753 

7 

0 

LCos 

d 

LCtn 

cd 

LTan 

LSin 

d 

'           Prop.  Pts. 

60°  —  Logarithms  of  Trigonometric  Functions 


76 


30°  —  Logarithms  of  Trigonometric  Functions          [ill 


/ 

LSin 

d 

LTan 

cd 

LCtn 

L  Cos 

d 

Prop.  Pts. 

0 

9.69  897 

9.76  144 

10.23  856 

9.93  753 

60 

1 

9.69  919 

22 

9.76  173 

29 

10.23  827 

9.93  746 

7 

59 

2 

9.69  941 

22 

9.76  202 

29 

10.23  798 

9.93738 

8 

58 

30 

29 

3 

9.69  963 

22 

9.76231 

29 

10.23  769 

9.93731 

7 

57 

2 

6  0 

5  8 

4 

9.69  984 

21 
22 

9.76  261 

30 
29 

10.23  739 

9.93  724 

7 
7 

56 

3 

9.0 

8.7 

5 

9.70  006 

9.76  290 

10.23  710 

9.93  717 

55 

4 

12.0 

11.6 

6 

9.70  028 

22 

9.76319 

29 

10.23  681 

9.93709 

8 

54 

5 

15.0 

14.5 

7 

9.70  050 

22 

9.76  348 

29 

10.23  652 

9.93702 

7 

53 

6 

18.0 

17.4 

8 

9.70  072 

22 

9.76  377 

29 

10.23  623 

9.93  695 

7 

52 

7 

21.0 

20.3 

9 

9.70  093 

21 

9.76  406 

29 

10.23  594 

9.93  687 

8 

51 

8 

24.0 

23.2 

10 

9.70  115 

22 

9.76  435 

29 

10.23  565 

9.93  680 

7 

50 

9 

27.0 

26.1 

11 

9.70  137 

22 

9.76  464 

29 

10.23  536 

9.93  673 

7 

49 

12 

9.70  159 

22 

9.76  493 

29 

10.23  507 

9.93665 

8 

48 

13 

9.70  180 

21 

9.76  522 

29 

10.23478 

9.93  658 

7 

47 

ao 

2EI 

14 

9.70  202 

22 

9.76551 

29 

10.23  449 

9.93  650 

8 

46 

2 

5.6 

4.4 

15 

9.70  224 

22 

9.76  580 

29 

10.23  420 

9.93  643 

7 

45 

3 

8.4 

6.6 

16 

9.70  245 

21 

9.76  609 

29 

10.23  391 

9.93  636 

7 

44 

4 

11.2 

8.8 

17 

9.70  267 

22 

9.76  639 

30 

10.23  361 

9.93  628 

8 

43 

5 

14.0 

11.0 

18 

9.70  288 

21 

9.76  668 

29 

10.23  332 

9.93  621 

7 

42 

6 

16.8 

13.2 

19 

9.70  310 

22 

9.76  697 

29 

10.23  303 

9.93  614 

7 

41 

7 

19.6 

15.4 

22 

28 

g 

g 

22 

4. 

17.6 

20 

9.70  S32 

9.76  725 

10.23  275 

9.93  606 

40 

9 

9K  9 

1Q  « 

21 

9.70  353 

21 

9.76  754 

29 

10.23  246 

9.93  599 

7 

39 

22 

9.70  375 

22 

9.76  783 

29 

10.23217 

9.93591 

8 

38 

23 

9.70  396 

21 

9.76812 

29 

10.23  188 

9.93  584 

7 

37 

21 

8 

24 

9.70  418 

22 

21 

9.76  841 

29 
29 

10.23  159 

9.93  577 

7 

8 

36 

2 

4.2 

1.6 

25 

9.70  439 

9.76  870 

10.23  130 

9.93  569 

35 

3 

6.3 

2.4 

26 

9.70461 

22 

9.76  899 

29 

10.23  101 

9.93  562 

7 

34 

4 

8.4 

3.2 

27 

9.70  482 

21 

9.76  928 

29 

10.23  072 

9.93  554 

8 

33 

5 

10.5 

4.0 

28 

9.70  504 

22 

9.76  957 

29 

10.23  043 

9.93  547 

7 

32 

6 

12.6 

4.8 

29 

9.70  525 

21 
22 

9.76  986 

29 
29 

10.23014 

9.93  539 

8 
7 

31 

7 

14.7 

5.6 

30 

9.70  547 

9.77  015 

10.22  985 

19.93  532 

30 

8 

16.8 

6.4 

31 

9.70  568 

21 

9.77  044 

29 

10.22956 

9.93  525 

7 

29 

9 

18.9 

7.2 

32 

9.70  590 

22 

9.77  073 

29 

10.22  927 

9.93517 

8 

28 

33 

9.70611 

21 

9.77  101 

28 

10.22  899 

9.93  510 

7 

27 

34 

9.70  633 

22 

9.77  130 

29 

10.22  870 

9.93502 

8 

26 

7 

35 

9.70  654 

21 

9.77  159 

29 

10.22  841 

9.93495 

7 

25 

2 

1.4 

36 

9.70  675 

21 

9.77  188 

29 

10.22812 

9.93487 

8 

24 

3 

2.1 

37 

9.70  697 

22 

9.77217 

29 

10.22  783 

9.93  480 

7 

23 

4 

2.8 

38 

9.70718 

21 

9.77  246 

29 

10.22  754 

9.93472 

8 

22 

5 

3.5 

39 

9.70  739 

21 

9.77  27.4 

28 

10.22  726 

9.93465 

7 

21 

6 

4.2 

40 

9.70  761 

22 

9.77  3t>3 

29 

10.22  697 

9.93  457 

8 

20 

7 

4.9 

41 

9.70  782 

21 

9.77  332 

29 

10.22668 

9.93450 

7 

19 

8 

5.6 

42 

9.70  803 

21 

9.77361 

29 

10.22639 

9.93442 

8 

18 

9 

6.3 

43 

9.70  824 

21 

9.77  390 

29 

10.22610 

9.93435 

7 

17 

44 

9.70  846 

22 

9.77418 

28 

10.22582 

9.93427 

8 

16 

45 

9.70  867 

21 

9.77  447 

29 

10.22553 

9.93  420 

7 

15 

From  the  top: 

46 

9.70  888 

21 
01 

9.77  476 

29 

10.22524 

9.93412 

8 

14 

For  30°+  or  210°+, 

47 
48 
49 

9.70  909 
9.70931 
9.70  952 

Sfl 

22 
21 

9.77  505 
9.77  533 
9.77  562 

29 
28 
29 

10.22495 
10.22467 
10.22438 

9.93  405 
9.93  397 
9.93  390 

7 
8 
7 

13 
12 
11 

read  as  printed  ;  for 
120°+  or  300°+,  read 

50 

9.70  973 

21 

9.77  591 

29 

10.22409 

9.93  382 

8 

10 

co-function. 

51 

9.70  994 

21 

9.77619 

28 

10.22381 

9.93375 

7 

9 

52 

9.71  015 

21 

9.77  648 

29 

10.22352 

9.93  367 

8 

8 

53 

9.71  036 

21 

9.77  677 

29 

10.22323 

9.93  360 

7 

7 

From  the  bottom: 

54 

9.71  058 

22 
21 

9.77  706 

29 
28 

10.22294 

9.93352 

8 
g 

6 

For590+or2390+, 

55 

56 
57 

9.71  079 
9.71  100 
9.71  121 

21 
21 

9.77  734 
9.77  763 
9.77  791 

29 

28 

10.22266 
10.22237 
10.22209 

9.93  344 
9.93  337 
9.93  329 

7 
8 

5 

4 
3 

read  as  printed  ;  for 
149°+  or  329°+,  read 

58 

9.71  142 

21 

9.77  820 

29 

10.22  180 

9.93322 

7 

2 

co-function. 

59 

9.71  163 

21 

9.77  849 

29 

10.22151 

9.93314 

8 

1 

60 

9.71  184 

21 

9.77  877 

28 

10.22  123 

9.93  307 

7 

0 

LCos 

d 

LCtn 

cd 

LTan 

LSin 

d 

/ 

Prop.  Pts. 

59°  —  Logarithms  of  Trigonometric  Functions 


Ill]         31°  —  Logarithms  of  Trigonometric  Functions 


77 


' 

LSin 

d 

LTan 

cd 

L  Ctn 

LCos 

d 

Prop.  Pis. 

0 

9.71  184 

9.77  877 

10.22  123 

9.93  307 

60 

1 

9.71  205 

21 

9.77  906 

29 

10.22  094 

9.93  299 

8 

59 

2 

9.71  226 

21 

9.77  935 

29 

10.22065 

9.93  291 

S 

58 

3 

9.71  247 

21 

9.77  963 

28 

10.22  037 

9.93  284 

7 

57 

4 

9.71  268 

21 

9.77  992 

29 

10.22  008 

9.93276 

8 

56 

5 

9.71  289 

21 

9.78  020 

28 

10.21  980 

9.93  269 

7 

55 

29 

28 

6 

9.71310 

21 

9.78  049 

29 

10.21951 

9.93  261 

8 

54 

2 

5.8 

5.6 

7 

9.71  331 

21 

9.78  077 

28 

10.21  923 

9.93  253 

53 

3 

8.7 

8.4 

8 

9.71  352 

21 

9.78  106 

29 

10.21  894 

9.93  246 

7 

52 

4 

11.2 

9 

9.71  373 

21 
20 

9.78  135 

29 
28 

10.21  865 

9.93  238 

S 

51 

5 

14'.5 

u!o 

10 

9.71  393 

9.78  163 

10.21  837 

9.93  230 

50 

6 

17.4 

16.8 

11 

9.71414 

21 

9.78  192 

29 

10.21  808 

9.93  223 

7 

49 

7 

20.3 

19.6 

12 

9.71  435 

21 

9.78  220 

28 

10.21  780 

9.93215 

8 

48 

8 

23.2 

22.4 

13 

9.71  456 

21 

9.78  249 

29 

10.21751 

9.93  207 

S 

47 

9 

26.1 

25.2 

14 

9.71  477 

21 
21 

9.78  277 

28 
29 

10.21  723 

9.93200 

7 

8 

46 

15 

9.71  498 

9.78  306 

10.21  694 

9.93  192 

45 

16 

9.71519 

21 

9.78  334 

28 

10.21  666 

9.93  184 

8 

44 

91 

9fl 

17 

9.71  539 

20 

9.78  363 

29 

10.21  637 

9.93  177 

7 

43 

lU 

JM 

IS 

9.71  560 

21 

9.78  391 

28 

10.21  609 

9.93  169 

8 

42 

2 

4.2 

4.0 

19 

9.71  581 

21 

9.78419 

28 

10.21  581 

9.93  161 

S 

41 

3 

6.3 

6.0 

21 

29 

7 

4 

8  4 

8.0 

20 

21 

22 
23 

9.71  602 
9.71  622 
9.71  643 
9.71  664 

20 
21 
21 

9.78  448 
9.78  476 
9.78  505 
9.78  533 

28 
29 
28 

10.21  552 
10.21  524 
10.21  495 
10.21467 

9.93  154 
9.93  146 
9.93  138 
9.93  131 

S 
S 
7 

40 

39 
38 
37 

5 

6 
7 
g 

lo'.s 

12.6 
14.7 

IRC 

io!o 

12.0 
14.0 

24 

9.71  685 

21 
20 

9.78  562 

29 
28 

10.21438 

9.93  123 

8 
8 

36 

9 

xu.o 

18.9 

is!o 

25 

9.71  705 

9.78  590 

10.21410 

9.93  115 

35 

20 

9.71  726 

21 

9.78618 

28 

10.21  382 

9.93  108 

7 

34 

27 

9.71  747 

21 

9.78  647 

29 

10.21  353 

9.93  100 

8 

33 

28 

9.71  767 

20 

9.78  675 

28 

10.21325 

9.93  092 

S 

32 

8 

7 

29 

9.71  788 

21 

9.78  704 

29 

10.21  296 

9.93  084 

8 

31 

2 

1.6 

1.4 

30 

9.71  809 

21 

9.78  732 

28 

10.21  268 

9.93  077 

7 

30 

3 

2.4 

2.1 

31 

9.71  829 

20 

9.78  760 

28 

10.21  240 

9.93  069 

8 

29 

4 

3.2 

2.8 

32 

9.71  850 

21 

9.78  789 

29 

10.21211 

9.93  061 

8 

28 

5 

4.0 

3.5 

33 

9.71  870 

20 

9.78  817 

28 

10.21  183 

9.93053 

S 

27 

6 

4.8 

4.2 

34 

9.71  891 

21 

9.78  845 

28 

10.21  155 

9.93  046 

7 

26 

7 

5.6 

4.9       ' 

35 

9.71911 

20 

9.78  874 

29 

10.21  126 

9.93  038 

S 

25 

8 

6.4 

*7  O 

5.6 

£*     O 

36 

9.71  932 

21 

9.78  902 

28 

10.21  098 

9.93  030 

8 

24 

7.2 

o.o 

37 

9.71  952 

20 

9.78  930 

28 

10.21  070 

9.93022 

8 

23 

38 

9.71  973 

21 

9.78  959 

29 

10.21  041 

9.93  014 

S 

22 

39 

9.71  994 

21 

9.78  987 

28 

10.21013 

9.93007 

7 

21 

40 

9.72  014 

20 

9.79  015 

28 

10.20985 

9.92999 

8 

20 

41 

9.72  034 

20 

9.79  043 

28 

10.20957 

9.92991 

8 

19 

42 

9.72  055 

21 

9.79  072 

29 

10.20928 

9.92  983 

S 

18 

From  the  top: 

43 

44 

9.72  075 
9.72  096 

20 
21 

9.79  100 
9.79  128 

28 
28 

10.20900 
10.20872 

9.92976 
9.92  968 

7 
8 

17 
16 

For310+or211°-|-) 

45 

9.72  116 

20 

9.79  156 

28 

10.20844 

9.92960 

8 

15 

read  as  printed;  for 

46 

9.72  137 

21 

9.79  185 

29 

10.20815 

9.92952 

8 

14 

121°+  or  301°+,  read 

47 

9.72  157 

20 

9.79  213 

28 

OQ 

10.20787 

9.92  944 

8 

13 

co-function. 

48 

9.72177 

2(J 

9.79  241 

Ja 

10.20759 

9.92  936 

8 

12 

49 

9.72  198 

21 

9.79  269 

28 

10.20731 

9.92929 

7 

11 

50 

9.72  218 

20 

9.79  297 

28 

10.20703 

9.92  921 

S 

10 

From  the  bottom: 

51 

9.72  238 

20 
01 

9.79  326 

29 

10.20674 

9.92913 

8 

9 

For58°+or2380+, 

52 
53 
54 

9.72  259 
9.72  279 
9.72  299 

21 

20 
20 

9.79  354 
9.79  382 
9.79410 

28 
28 

10.20646 
10.20618 
10.20  590 

9.92905 
9.92  897 
9.92  889 

8 
8 
S 

8 
7 
6 

read  as  printed  ;  for 
148°+  or  3280-1-,  read 

55 

9.72  320 

21 

9.79  438 

28 

10.20562 

9.92  881 

8 

5 

co-function. 

56 

9.72  340 

20 

9.79  466 

28 

10.20534 

9.92  874 

7 

4 

57 

9.72  360 

20 

9.79  495 

29 

10.20505 

9.92  866 

8 

3 

58 

9.72  381 

21 

9.79  523 

28 

10.20477 

9.92858 

S 

2 

59 

9.72  401 

20 
20 

9.79  551 

28 
28 

10.20449 

9.92  850 

8 
8 

1 

60 

9.72  421 

9.79  579 

10.20421 

9.92  842 

0 

LCos 

d 

LCtn 

cd 

LTan 

LSin 

d 

' 

Prop.  Pts. 

58°  —  Logarithms  of  Trigonometric  Functions 


78 


32°  —  Logarithms  of  Trigonometric  Functions          [III 


' 

LSin 

d 

LTan 

cd 

L  Ctn 

L  Cos 

d 

Prop.  Pts. 

0 

9.72421 

9.79  579 

10.20421 

9.92842 

60 

1 

9.72  441 

20 

9.79  607 

28 

10.20393 

9.92834 

8 

59 

2 

9.72  461 

20 

9.79  635 

28 

10.20365 

9.92826 

8 

58 

29 

28 

3 

9.72  482 

21 

9.79  663 

28 

10.20337 

9.92818 

8 

57 

2 

5.8 

5.6 

4 

9.72  502 

20 
20 

9.79  691 

28 
28 

10.20309 

9.92810 

7 

56 

3 

8.7 

8.4 

5 

9.72  522 

9.79  719 

10.20281 

9.92  803 

55 

4 

11.6 

11.2  ' 

6 

9.72  542 

20 

9.79  747 

28 

10.20253 

9.92795 

8 

54 

5 

14.5 

14.0 

7 

9.72  562 

20 

9.79  776 

29 

10.20  224 

9.92787 

8 

53 

6 

17.4 

16.8 

8 

9.72  582 

20 

9.79  804 

28 

10.20  196 

9.92779 

8 

52 

7 

20.3 

19.6 

9 

9.72  602 

20 

9.79  832 

28 

10.20  168 

9.92771 

8 

51 

8 

23.2 

22.4 

10 

9.72  622 

20 

9.79  860 

28 

10.20  140 

9.92  763 

8 

50 

9 

26.1 

25.2 

11 

9.72  643 

21 

9.79  888 

28 

10.20112 

9.92755 

8 

49 

12 

9.72  663 

20 

9.79  916 

28 

10.20  084 

9.92  747 

8 

48 

OT 

01 

13 

9.72  683 

20 

9.79  944 

28 

10.20056 

9.92739 

8 

47 

27 

21 

14 

9.72  703 

20 

9.79  972 

28 

10.20  028 

9.92731 

8 

46 

2 

5.4 

4.2 

15 

9.72  723 

20 

9.80  000 

28 

10.20  000 

9.92  723 

8 

45 

3 

8.1 

6.3 

16 

9.72  743 

20 

9.80  028 

28 

10.19972 

9.92715 

8 

44 

4 

10.8 

8.4 

17 

9.72  763 

20 

9.80  056 

28 

10.19944 

9.92707 

8 

43 

5 

13.5 

10.5 

18 

9.72  783 

20 

9.80  084 

28 

10.19916 

9.92  699 

8 

42 

6 

16.2 

12.6 

19 

9.72  803 

20 

9.80  112 

28 

10.19888 

9.92691 

8 

41 

7 

18.9 

14.7 

20 

28 

8 

8 

21.6 

16.8 

20 

9.72  823 

9.80  140 

10.19  860 

9.92  683 

40 

9 

24.3 

18.9 

21 

9.72  843 

20 

9.80  168 

2o 

10.19832 

9.92675 

8 

39 

22 

9.72  863 

20 

9.80  195 

27 

10.19  805 

9.92  667 

8 

38 

23 

9.72  883 

20 

9.80  223 

28 

10.19777 

9.92  659 

8 

37 

20 

19 

24 

9.72  902 

19 
20 

9.80  251 

28 
28 

10.19749 

9.92651 

8 
8 

36 

2 

4.0 

3.8 

25 

9.72  922 

9.80  279 

10.19721 

9.92  643 

35 

3 

6.0 

5.7 

26 

9.72  942 

20 

9.80  307 

28 

10.19693 

9.92  635 

8 

34 

4 

8.0 

7.6 

27 

9.72  962 

20 

9.80  335 

28 

10.19665 

9.92627 

8 

33 

5 

10.0 

9.5 

28 

9.72  982 

20 

9.80  363 

28 

OQ 

10.19637 

9.92  619 

8 

32 

6 

12.0 

11.4 

29 

9.73  002 

20 
20 

9.80  391 

ma 

28 

10.19609 

9.92611 

8 
8 

31 

7 

14.0 

13.3 

30 

9.73  022 

9.80  419 

10.19  581 

9.92  603 

30 

8 

16.0 

15.2 

31 

9.73  041 

19 

9.80  447 

28 

10.19553 

9.92  595 

8 

29 

9 

18.0 

17.1 

32 

9.73  061 

20 

9.80  474 

27 

10.19526 

9.92  587 

8 

28 

33 

9.73  081 

20 

9.80  502 

28 

10.19498 

9.92579 

8 

27 

34 

9.73  101 

20 

9.80  530 

28 

10.19470 

9.92571 

8 

26 

9      a     Y 

35 

9.73  121 

20 

9.80  558 

28 

10.19442 

9.92563 

8 

25 

2 

1.8    1.6    1.4 

36 

9.73  140 

19 

9.80  586 

28 

10.19414 

9.92  555 

8 

24 

3 

2.7  -2.4    2.1 

37 

9.73  160 

20 

9.80  614 

28 

10.19386 

9.92  546 

9 

23 

4 

3.6    3.2    2.8 

38 

9.73  180 

20 

9.80  642 

28 

10.19358 

9.92538 

8 

22 

5 

4.5    4.0    3.5 

39 

9.73  200 

20 

9.80  669 

27 

10.19331 

9.92  530 

8 

21 

6 

5.4    4.8    4.2 

40 

9.73  219 

19 

9.80  697 

28 

10.19303 

9.92  522 

8 

20 

7 

6.3    5.6    4.9 

7O      A  A      Ci  A 

41 

9.73  239 

20 

9.80  725 

28 

10.19275 

9.92514 

8 

19 

tA       O.T;       O.O 
81       79      A  Q 

42 

9.73  259 

20 

9.80  753 

28 

10.19247 

9.92506 

8 

18 

.1       {  mm      O.O 

43 

9.73  278 

19 

9.80  781 

28 

10.19219 

9.92498 

8 

17 

44 
45 

9.73  298 
9.73  318 

20 
20 

9.80  808 
9.80  836 

27 
28 

10.19  192 
10.19  164 

9.92490 
9.92482 

8 
8 

16 
15 

From  the  top: 

46 

9.73  337 

19 

9.80  864 

28 

10.19  136 

9.92473 

9 

14 

For32°+or2120+, 

47 
48 
49 

9.73  357 
9.73  377 
9.73  396 

20 
20 
19 

9.80  892 
9.80919 
9.80  947 

28 
27 
28 

10.19  108 
10.19081 
10.19053 

9.92  465 
9.92457 
9.92449 

8 
8 
S 

13 
12 
11 

read  as  printed;  for 
122°+  or  302°+,  read 

50 

9.73  416 

20 

9.80  975 

28 

10.19025 

9.92441 

8 

10 

co-function. 

51 

9.73  435 

19 

9.81  003 

28 

10.18997 

9.92433 

8 

9 

52 
53 

9.73  455 
9.73  474 

20 
19 

9.81  030 
9.81  058 

27 

28 

10.18970 
10.18942 

9.92425 
9.92416 

8 

g 

8 
7 

From  the  bottom: 

54 
55 

56 
57 

^•73494^ 
9!73~513 
9.73  533 
9.73  552 

20 
19 
20 
19 

9.81  086 

9.81  113 
9.81  141 
9.81  169 

28 
27 
28 
28 

10.18914 
10.18887 
10.18859 
10.18831 

9.92408 
9.92400 
9.92392 
9.92  384 

8 
8 

8 

S 

6 
5 
4 
3 

For  57°+  or  237°+, 

read  as  printed  ;  for 
147°+  or  327°+,  read 

58 

9.73  572 

20 

9.81  196 

27 

10.18804 

9.92  376 

8 

2 

co-function. 

59 

9.73  591 

19 
20 

9.81  224 

28 
28 

10.18776 

9.92367 

8 

1 

60 

9.73611 

9.81  252 

10.18748 

9.92  359 

0 

LCos 

d 

LCtn 

c  d      L  Tan 

L  Sin 

d 

' 

Prop.  Pts. 

57°  —  Logarithms  of  Trigonometric  Functions 


Ill]         33°  —  Logarithms  of  Trigonometric  Functions 


79 


' 

LSin 

d 

LTan 

cd 

LCtn 

LCos 

d 

Prop.  Pts. 

0 

9.73611 

9.81  252 

10.18748 

9.92  359 

60 

1 

9.73  630 

19 

9.81  279 

27 

10.18721 

9.92351 

8 

59 

2 

9.73  650 

20 

9.81  307 

28 

10.18693 

9.92  343 

8 

58 

28 

27 

3 

9.73  669 

19 

9.81  335 

28 

10.18665 

9.92335 

S 

57 

2 

5.6 

5.4 

4 

9.73  689 

20 
19 

9.81  362 

27 
28 

10.18638 

9.92  326 

9 

g 

56 

3 

8.4 

8.1 

5 

9.73  708 

9.81  390 

10.18610 

9.92318 

55 

4 

11.2 

10.8 

6 

9.73  727 

19 

9.81  418 

28 

10.18582 

9.92310 

S 

54 

5 

14.0 

13.5 

7 

9.73  747 

20 

9.81  445 

27 

10.18555 

9.92  302 

S 

53 

6 

16.8 

16.2 

8 

9.73  766 

19 

9.81  473 

28 

10.18527 

9.92  293 

9 

52 

7 

19.6 

18.9 

9 

9.73  785 

19 

9.81  500 

27 

10.18500 

9.92  285 

S 

51 

8 

22.4 

21.6 

10 

9.73  805 

20 

9.81  528 

28 

10.18472 

9.92  277 

S 

50 

9 

25.2 

24.3 

11 

9.73  824 

19 

9.81  556 

28 

10.18444 

9.92  269 

8 

49 

12 

9.73  843 

19 

9.81  583 

27 

10.18417 

9.92260 

9 

48 

OA           *n 

13 

9.73  863 

20 

9.81611 

28 

10.18389 

9.92252 

8 

47 

20 

•* 

14 

9.73  882 

19 

9.81  638 

27 

10.18362 

9.92  244 

S 

46 

2 

4.0 

3.8 

15 

9.73  901 

19 

9.81  666 

28 

10.18334 

9.92  235 

9 

45 

3 

6.0 

5.7 

16 

9.73  921 

20 

9.81  693 

27 

10.18307 

9.92  227 

S 

44 

4 

8.0 

7.6 

17 

9.73  940 

19 

9.81  721 

28 

10.18279 

9.92219 

S 

43 

5 

10.0 

9.5 

18 

9.73  959 

19 

9.81  748 

27 

10.18252 

9.92211 

S 

42 

6 

12.0 

11.4 

19 

9.73  978 

19 

9.81  776 

28 

10.18224 

9.92  202 

9 
g 

41 

7 
8 

14.0 
16.0 

13.3 

20 

9.73  997 

9.81  803 

10.18  197 

9.92  194 

40 

9 

18.0 

17^1 

21 

9.74  017 

20 

9.81  831 

28 

10.18169 

9.92  186 

8 

39 

22 

9.74  036 

19 

9.81  858 

27 

10.18  142 

9.92  177 

9 

38 

23 

9.74  055 

19 

9.81  886 

28 

10.18114 

9.92  169 

8 

37 

18 

9 

24 

9.74  074 

19 
19 

9.81  913 

27 
28 

10.18087 

9.92  161 

8 
9 

36 

2 

3.6 

1.8 

25 

9.74  093 

9.81  941 

10.18059 

9.92  152 

35 

3 

5.4 

2.7 

26 

9.74  113 

20 

9.81  968 

27 

10.18032 

9.92  144 

8 

34 

4 

7.2 

3.6 

27 

9.74  132 

19 

9.81  996 

28 

10.18004 

9.92  136 

8 

33 

5 

9.0 

4.5 

28 

9.74  151 

19 

9.82  023 

27 

10.17977 

9.92  127 

9 

32 

6 

10.8 

5.4 

29 

9.74  170 

19 
19 

9.82  051 

28 
27 

10.17949 

9.92119 

S 
g 

31 

7 

12.6 

6.3 

30 

9.74  189 

9.82  078 

10.17922 

9.92111 

30 

8 

14.4 

7.2 

31 

9.74  208 

19 

9.82  106 

28 

10.17  894 

9.92  102 

9 

29 

9 

16.2 

8.1 

32 

9.74  227 

19 

9.S2  133 

27 

10.17867 

9.92  094 

8 

28 

33 

9.74  246 

19 

9.82  161 

28 

10.17839 

9.92  086 

8 

27 

34 

9.74  265 

19 

9.82  188 

27 

10.17812 

9.92  077 

9 

26 

8 

35 

9.74  284 

19 

9.82  215 

27 

10.17785 

9.92069 

8 

25 

2    1.6 

36 

9.74  303 

19 

9.82  243 

28 

10.17757 

9.92  060 

9 

24 

3    2.4 

37 

9.74  322 

19 

9.82270 

27 

10.17730 

9.92052 

S 

23 

4    3.2 

38 

9.74  341 

19 

9.82  298 

28 

10.17702 

9.92  044 

8 

22 

6    4.0 

39 

9.74  360 

19 

9.82  325 

27 

10.17675 

9.92035 

9 

21 

6    4.8 

40 

9.74  379 

19 

9.82  352 

27 

10.17  648 

9.92  027 

S 

20 

7    5.6 

8      A  A 

41 

9.74  398 

19 

9.82  380 

28 

10.17620 

9.92018 

9 

ia 

D.4 

9*7   O 

42 

9.74  417 

19 

9.82  407 

27 

10.17593 

9.92010 

S 

18 

7.4 

43 

9.74  436 

19 

9.82  435 

28 

10.17565 

9.92002 

8 

17 

44 
45 

9.74  455 
9.74  474 

19 
19 

9.82  462 
9.82  489 

27 

27 

10.17538 
10.17511 

9.91  993 
9.91  985 

9 

8 

16 
15 

From  the  top: 

46 

9.74  493 

19 

9.82517 

28 

10.17483 

9.91976 

9 

14 

For330+or2138+, 

47 
48 
49 

9.74512 
9.74  531 
9.74  549 

19 
19 
18 

9.82  544 
9.82  571 
9.82  599 

27 

27 
28 

10.17456 
10.17429 
10.17401 

9.91  968 
9.91  959 
9.91951 

8 
9 
8 

13 
12 
11 

read  as  printed;  for 
1230+or303°-t-,read 

50 

9.74  568 

19 

9.82  626 

27 

10.17374 

9.91  942 

9 

10 

co-function. 

51 

9.74  587 

19 

9.82  653 

27 

10.17  347 

9.91934 

8 

9 

52 
53 

9.74  606 
9.74  625 

19 
19 

9.82  681 
9.82  708 

28 
27 

10.17319 
10.17292 

9.91925 
9.91917 

9 

S 

8 
7 

From  the  bottom: 

54 

9.74  644 

19 
18 

9.82  735 

27 
27 

10.17265 

9.91908 

9 

S 

6 

For56°-(-or2360+, 

55 

56 
57 

9.74  662 
9.74  681 
9.74  700 

19 

19 

9.82762 
9.82  790 
9.82  817 

28 
27 

10.17238 
10.17210 
10.17183 

9.91  900 
9.91  891 
9.91  883 

9 

8 

5 

4 
3 

read  as  printed  ;  for 
146°+  or  326°+  read 

58 

9.74719 

19 

9.82  844 

27 

10.17  156 

9.91  874 

9 

2 

co-function. 

59 

9.74  737 

18 

9.82  871 

27 

10.17  129 

9.91866 

8 

1 

60 

9.74  756 

19 

9.82  89S 

28 

10.17101 

9.91  857 

9 

0 

LCos 

d 

L  Ctn     cd      LTan 

L  Sin 

d 

Prop.  Pts. 

56°  —  Logarithms  of  Trigonometric  Functions 


80 


34°  —  Logarithms  of  Trigonometric  Functions          [in 


' 

LSin 

d 

LTan 

cd 

LCtn 

L  Cos 

d 

Prop.  Pts. 

0 

9.74  756 

9.82  899 

10.17101 

9.91  857 

60 

1 

9.74  775 

19 

9.82  926 

27 

10.17074 

9.91  849 

8 

59 

2 

9.74  794 

19 

9.82  953 

27 

10.17047 

9.91840 

9 

58 

28 

27 

3 

9.74  812 

18 

9.82  980 

27 

10.17020 

9.91  832 

8 

57 

5t* 

4 

9.74  831 

19 
19 

9.83  008 

28 
27 

10.16992 

9.91  823 

9 

56 

3 

.D 

8.4 

8.1 

5 

9.74  850 

9.83  035 

10.16965 

9.91815 

55 

4 

11.2 

10.8 

6 

9.74  868 

18 

9.83  062 

27 

10.16938 

9.91  806 

9 

54 

5 

14.0 

13.5 

7 

9.74  887 

19 

9.83  089 

27 

10.16911 

9.91  798 

8 

53 

6 

16.8 

16.2 

8 

9.74  906 

19 

9.83  117 

28 

10.16883 

9.91  789 

9 

52 

7 

19.6 

18.9 

9 

9.74  924 

18 

9.83  144 

27 

10.16856 

9.91  781 

8 

51 

8 

22.4 

21.6 

10 

9.74  943 

19 

9.83  171 

27 

10.16829 

9.91  772 

9 

50 

9 

25.2 

24.3 

11 

9.74  961 

18 

9.83  198 

27 

10.16802 

9.91763 

9 

49 

12 

9.74  980 

19 

9.83  225 

27 

10.16775 

9.91  755 

8 

48 

13 

9.74  999 

19 

9.83  252 

27 

10.16748 

9.91  746 

9 

47 

20 

19 

14 

9.75  017 

18 

9.83  280 

28 

10.16720 

9.91  738 

8 

46 

2 

5.2 

3.8 

15 

9.75  036 

19 

9.83  307 

27 

10.16693 

9.91  729 

9 

45 

3 

7.8 

5.7 

16 

9.75  054 

18 

9.83  334 

27 

10.16666 

9.91720 

9 

44 

4 

10.4 

7.6 

17 

9.75  073 

19 

9.83  361 

27 

10.16639 

9.91712 

8 

43 

5 

13.0 

9.5 

18 

9.75  091 

18 

9.83  388 

27 

10.16612 

9.91  703 

9 

42 

6 

15.6 

11.4 

19 

9.75  110 

19 

9.83  415 

27 

10.16585 

9.91  695 

8 

41 

7 

18.2 

13.3 

20 

21 

9.75  128 
9.75  147 

19 

9.83  442 
9.83  470 

28 

10.16558 
10.16530 

9.91  686 
9.91  677 

9 
9 

40 

39 

8 
9 

20.8 
23.4 

15.2 
17.1 

22 

9.75  165 

18 

9.83  497 

27 

10.16503 

9.91  669 

8 

38 

23 

9.75  184 

19 

9.83  524 

27 

10.16476 

9.91660 

9 

37 

18 

q 

24 

9.75  202 

18 
19 

9.83  551 

27 
27 

10.16449 

9.91651 

9 

8 

36 

2 

3.6 

V 

1.8 

25 

9.75  221 

1  Q 

9.83  578 

10.16422 

9.91  643 

35 

3 

5.4 

2.7 

26 

9.75  239 

18 

9.83  605 

27 

10.16395 

9.91634 

9 

34 

4 

7.2 

3.6 

27 

9.75  258 

19 

9.83  632 

27 

10.16368 

9.91  625 

9 

33 

5 

9.0 

4.5 

28 

9.75  276 

18 

1  Q 

9.83  659 

27 

10.16341 

9.91617 

8 

32 

6 

iols 

5  4 

29 

9.75  294 

lo 

19 

9.83  686 

27 

27 

10.16314 

9.91608 

9 
g 

31 

7 

12.6 

6.3 

30 

9.75  313 

9.83  713 

10.16287 

9.91  599 

30 

8 

14.4 

7.2 

31 

9.75  331 

18 

9.83  740 

27 

10.16260 

9.91591 

8 

29 

9 

16.2 

8.1 

32 

9.75  350 

19 

9.83  768 

28 

10.16232 

9.91582 

9 

28 

33 

9.75  368 

18 

9.83  795 

27 

10.16205 

9.91573 

9 

27 

34 

9.75  386 

18 
19 

9.83  822 

27 
27 

10.16  178 

9.91565 

8 
9 

26 

8 

35 

9.75  405 

9.83  849 

10.16151 

9.91656 

25 

2    1.6 

30 

9.75  423 

18 

9.83  876 

27 

10.16124 

9.91  547 

9 

24 

3    2.4 

37 

9.75  441 

18 

9.83  903 

27 

10.16097 

9.91538 

9 

23 

4    3.2 

38 

9.75  459 

18 

9.83  930 

27 

10.16070 

9.91530 

8 

22 

5    4.0 

39 

9.75  478 

19 

9.83  957 

27 

10.16043 

9.91521 

9 

21 

6    4.8 

40 

9.75  496 

18 

9.83  984 

27 

10.16016 

9.91512 

9 

20 

7    5.6 

41 

9.75514 

18 

9.84011 

27 

10.15989 

9.91504 

8 

19 

8    6.4 

42 

9.75  533 

19 

9.84  038 

27 

10.15962 

9.91495 

9 

18 

9    7.2 

43 

9.75  551 

18 

9.84  065 

27 

10.15935 

9.91486 

9 

17 

44 

9.75  569 

18 

9.84  092 

27 

10.15908 

9.91477 

9 

16 

45 

9.75  587 

18 

9.84  119 

27 

10.15881 

9.91  469 

8 

15 

From  the  top: 

40 

9.75  605 

18 

9.84  146 

27 

10.15854 

9.91460 

9 

14 

For34°-(-or2140+, 

47 
48 
49 

9.75  624 
9.75  642 
9.75  660 

19 
18 
18 

9.84  173 
9.84  200 
9.84  227 

27 
27 
27 

10.15827 
10.15800 
10.15773 

9.91451 
9.91442 
9.91433 

9 
9 
9 

13 
12 
11 

read  as  printed  ;  for 
124°+  or  304°+,  read 

50 

9.75  678 

18 

9.84  254 

27 

10.15746 

9.91425 

8 

10 

co-function. 

51 

9.75  696 

18 

9.84  280 

26 

10.15720 

9.91416 

9 

9 

52 

9.75  714 

18 

9.84  307 

27 

10.15693 

9.91407 

9 

8 

53 

9.75  733 

19 

9.84  334 

27 

10.15666 

9.91398 

9 

7 

From  the  bottom: 

54 

9.75  751 

18 
18 

9.84  361 

27 
27 

10.15639 

9.91389 

9 

8 

6 

For  55°+  or  235°+, 

55 

50 
57 

9.75  769 
9.75  787 
9.75  805 

18 
18 

9.84  388 
9.84415 
9.84  442 

27 
27 

10.15612 
10.15585 
10.15558 

9.91  381 
9.91372 
9.91363 

9 
9 

5 

4 
3 

read  as  printed  ;  for 
1450+or325°-f,read 

58 

9.75  823 

18 

9.84  469 

27 

10.15531 

9.91354 

9 

2 

co-function. 

59 

9.75  841 

18 

9.84  496 

27 

10.15504 

9.91  345 

9 

1 

60 

9.75  859 

18 

9.84  523 

27 

10.15477 

9  91  336 

J 

0 

LCos 

d 

LCtn 

cd 

LTan 

LSin 

d 

' 

Prop.  Pts. 

55°  —  Logarithms  of  Trigonometric  Functions 


Ill]         35°  —  Logarithms  of  Trigonometric  Functions 


81 


/ 

LSin 

d 

LTan 

cd 

L  Ctn 

LCos 

d 

Prop.  Pts. 

0 

9.75  859 

9.84  523 

10.15477 

9.91  336 

60 

1 

9.75877 

18 

9.84550 

27 

10.15450 

9.91328 

s 

59 

2 

9.75  895 

18 

9.84576 

26 

10.15424 

9.91319 

9 

58 

27 

26 

3 

9.75913 

18 

9.84  603 

27 

10.15397 

9.91310 

9 

57 

2 

5.4 

5.2 

4 

9.75931 

18 
18 

9.84630 

27 
27 

10.15370 

9.91301 

9 
9 

56 

3 

8.1 

7.8 

5 

9.75  949 

9.84  657 

10.15  343 

9.91292 

55 

4 

10.8 

10.4 

6 

9.75967 

18 

9.84684 

27 

10.15316 

9.91283 

9 

54 

5 

13.5 

13.0 

7 

9.75  985 

18 

9.84711 

27 

10.15289 

9.91274 

9 

53 

6 

16.2 

15.6 

8 

9.76  003 

IS 

9.84738 

27 

10.15262 

9.91266 

8 

52 

7 

18.9 

18.2 

9 

9.76021 

18 

9.84764 

26 

10.15236 

9.91  257 

9 

51 

8 

21.6 

20.8 

10 

9.76  039 

18 

9.84791 

27 

10.15  209 

9.91  248 

9 

50 

9 

24.3 

23.4 

11 

9.76057 

18 

9.84  8ia 

27 

10.15  182 

9.91  239 

9 

49 

12 

9.76075 

18 

9.S4S45 

27 

10.15155 

9.91230 

9 

48 

•f  O 

•1  T 

13 

9.76093 

18 

9.84  87*  < 

i  27 

10.15128 

9.91221 

9 

47 

18 

17 

14 

9.76111 

18 

9.84  899 

27 

10.15  101 

9.91212 

9 

46 

2 

3.6 

3.4 

15 

9.76  129 

18 

9.84  925 

26 

10.15  075 

9.91  203 

9 

45 

3 

5.4 

5.1 

16 

9.76  146 

17 

9.84  952 

27 

10.15  048 

9.91  194 

9 

44 

4 

7.2 

6.8 

17 

9.76  164 

18 

9.84979 

27 

10.15021 

9.91  185 

9 

43 

5 

9.0 

8.5 

18 

9.76  182 

18 

9.85  006 

27 

10.14994 

9.91  176 

9 

42 

6 

10.8 

10.2 

19 

9.76200 

18 

9.85  033 

27 

10.14967 

9.91  167 

9 

41 

7 

12.6 

11.9 

18 

26 

9 

3 

14.4 

13.6 

20 

9.76218 

9.85  059 

O*7 

10.14941 

9.91  158 

40 

9 

16.2 

15.3 

21 

9.76  236 

18 

9.85  086 

£1 

10.14914 

9.91  149 

9 

39 

22 

9.76253 

17 

9.85  113 

27 

10.14887 

9.91  141 

S 

38 

23 

9.76271 

18 

9.85  140 

27 

10.14860 

9.91  132 

9 

37 

10 

9 

24 

9.76289 

18 
18 

9.85  166 

26 
27 

10.14834 

9.91  123 

9 
9 

36 

2 

2.0 

1.8 

25 

9.76307 

9.85  193 

10.14807 

9.91  114 

35 

3 

3.0 

2.7 

26 

9.76324 

17 

9.85  220 

27 

10.14780 

9.91  105 

9 

34 

4 

4.0 

3.6 

27 

9.76342 

18 

f  Q 

9.85  247 

27 

OA 

10.14753 

9.91  096 

9 

33 

5 

5.0 

4.5 

28 

9.76360 

18 

9.85  273 

Jo 

10.14727 

9.91  087 

32 

6 

6.0 

5.4 

29 

9.76378 

18 
17 

9.85  300 

27 
27 

10.14700 

9.91078 

9 
9 

31 

7 

7.0 

6.3 

30 

9.76395 

9.85  327 

10.14673 

9.91  069 

30 

8 

8.0 

7.2 

31 

9.76413 

18 

9.85  354 

27 

10.14646 

9.91  060 

9 

29 

9 

9.0 

8.1 

32 

9.76431 

18 

9.85  380 

26 

10.14620 

9.91  051 

9 

28 

33 

9.76448 

17 

9.85407 

27 

10.14593 

9.91  042 

9 

27 

34 

9.76466 

18 

9.85  434 

27 

10.14566 

9.91033 

9 

26 

8 

35 

9.76484 

18 

9.85  460 

26 

10.14540 

9.91  023 

10 

25 

2    1.6 

36 

9.76501 

17 

9.85  487 

27 

10.14513 

9.91014 

9 

24 

3    2.4 

37 

9.76519 

18 

9.85514 

27 

10.14486 

9.91005 

9 

23 

4    3.2 

38 

9.76537 

IS 

9.85  540 

26 

10.14460 

9.90996 

9 

22 

5    4.0 

39 

9.76554 

17 

9.85  567 

27 

10.14433 

9.90  987 

9 

21 

6    4.8 

40 

9.76572 

18 

9.85  594 

27 

10.14406 

9.90978 

9 

20 

7    5.6 

41 

9.76590 

18 

9.85  620 

26 

10.14380 

9.90969 

9 

19 

8    6.4 

42 

9.76  607 

17 

9.85  647 

27 

10.14353 

9.90960 

9 

18 

9    7.2 

43 

9.76  625 

IS 

9.85  674 

27 

10.14326 

9.90951 

9 

17 

44 

9.76  642 

17 

9.85  700 

26 

10.14300 

9.90  942 

9 

16 

45 

9.76  660 

18 

9.85  727 

27 

10.14273 

9.90  933 

9 

15 

From  the  top: 

46 

9.76  677 

17 

9.85  754 

27 

10.14  246 

9.90  924 

9 

14 

For  35°+  or  215°+, 

47 
48 
49 

9.76  695 
9.76712 
9.76730 

18 
17 
18 

9.85  780 
9.85  807 
9.85  834 

26 
27 
27 

10.14220 
10.14193 
10.14166 

9.90915 
9.90906 
9.90  896 

9 

10 

13 
12 
11 

read  as  printed  ;  for 
1250+or3050+,read 

50 

9.76  747 

17 

9.85  860 

26 

10.14140 

9.90887 

9 

10 

co-function. 

51 

9.76  765 

18 

9.85  887 

27 

10.14113 

9.90  878 

9 

9 

52 

9.76782 

17 

9.85913 

26 

10.14087 

9.90869 

9 

8 

53 

9.76  800 

18 

9.85  940 

27 

10.14060 

9.90  860 

9 

7 

From  the  bottom: 

54 

9.76817 

17 
IS 

9.85  967 

27 
26 

10.14033 

9.90851 

9 

9 

6 

For  54°+  or  234°+, 

55 

56 
57 

9.76  835 
9.76  852 
9.76  870 

17 

18 

9.85  993 
9.86020 
9.86046 

27 

26 

10.14007 
10.13980 
10.13954 

9.90842 
9.90  832 
9.90  823 

10 
9 

5 

4 
3 

read  as  printed  ;  for 
144°+  or  324°+  read 

58 

9.76  887 

17 

9.86  073 

27 

10.13  927 

9.90814 

9 

2 

co-function. 

59 

9.76  904 

17 

9.86  100 

27 

10.13900 

9.90  805 

9 

T 

60 

9.76  922 

IS 

9.86126 

26 

10.13  874 

9.90  796 

9 

0 

LCos 

d 

LCtn 

cd 

L  Tan 

LSin 

d 

/ 

Prop.  Pts. 

54°  —  Logarithms  of  Trigonometric  Functions 


82 


36°  —  Logarithms  of  Trigonometric  Functions          [III 


LSin 

d 

LTan 

cd 

LCtn 

L  Cos 

d 

Prop.  Pts. 

0 

9.76  922 

9.86  126 

10.13874 

9.90796 

60 

1 

9.76  939 

17 

9.86  153 

27 

10.13847 

9.90787 

9 

59 

2 

9.76957 

18 

9.86  179 

26 

10.13821 

9.90777 

10 

58 

27 

26 

3 

9.76974 

17 

9.86206 

27 

10.13794 

9.90768 

9 

57 

2 

5  4 

5.2 

4 

9.76991 

17 
18 

9.86232 

26 
27 

10.13768 

9.90759 

9 
9 

56 

3 

8.1 

7.8 

5 

9.77009 

9.86259 

10.13741 

9.90750 

55 

4 

10.8 

10.4 

6 

9.77026 

17 

9.86285 

26 

10.13715 

9.90741 

9 

54 

5 

13.5 

13.0 

7 

9.77043 

17 

9.86312 

27 

10.13688 

9.90731 

10 

53 

6 

16.2 

15.6 

8 

9.77061 

18 

9.86338 

26 

10.13662 

9.90722 

9 

52 

7 

18.9 

18.2 

9 

9.77078 

17 

9.86365 

27 

10.13635 

9.90713 

9 

51 

8 

21.6 

20.8 

10 

9.77095 

17 

9.86392 

27 

10.13608 

9.90704 

9 

50 

9 

24.3 

23.4 

11 

9.77112 

17 

9.86418 

26 

10.13582 

9.90694 

10 

49 

12 

9.77  130 

18 

9.86445 

27 

10.13  555 

9.90685 

9 

48 

13 

9.77  147 

17 

9.86471 

26 

10.13529 

9.90676 

9 

47 

18 

11 

14 

9.77  164 

17 

9.86498 

27 

10.13502 

9.90  667 

9 

46 

2 

3.6 

3.4 

15 

9.77  181 

17 

9.86524 

26 

10.13476 

9.90  657 

10 

45 

3 

5.4 

5.1 

16 

9.77  199 

18 

9.86551 

27 

10.13449 

9.90648 

9 

44 

4 

7.2 

6.8 

17 

9.77216 

17 

9.86577 

26 

10.13423 

9.90639 

9 

43 

5 

9.0 

8.5 

18 

9.77233 

17 

9.86603 

26 

10.13397 

9.90630 

9 

42 

6 

10.8 

10.2 

19 

9.77250 

17 

9.86630 

27 

10.13370 

9.90620 

10 

41 

7 

12.6 

11.9 

18 

26 

9 

8 

14.4 

13.6 

20 

9.77268 

9.86  656 

10.13344 

9.90611 

40 

g 

16.2 

15.3 

21 

9.77  285 

17 

9.86  683 

27 

10.13317 

9.90  602 

9 

39 

22 

9.77302 

17 

9.86709 

26 

10.13291 

9.90592 

10 

38 

23 

9.77319 

17 

9.86736 

27 

10.13264 

9.90583 

9 

37 

16 

10 

24 

9.77336 

17 
17 

9.86762 

26 
27 

10.13238 

9.90574 

9 
9 

36 

2 

3.2 

2.0 

25 

9.77353 

9.86789 

10.13211 

9.90565 

35 

3 

4.8 

3.0 

26 

9.77370 

17 

9.86815 

26 

10.13  185 

9.90555 

10 

34 

4 

6.4 

4.0 

27 

9.77387 

17 

9.86842 

27 

10.13  158 

9.90546 

9 

33 

5 

8.0 

5.0 

28 

9.77405 

18 

9.86868 

26 

10.13132 

9.90537 

9 

32 

6 

9.6 

6.0 

29 

9.77422 

17 
17 

9.86894 

26 
27 

10.13  106 

9.90527 

10 
9 

31 

7 

11.2 

7.0 

30 

9.77439 

9.86921 

10.13  079 

9.90518 

30 

8 

12.8 

8.0 

31 

9.77456 

17 

9.86  947 

26 

10.13053 

9.90509 

9 

29 

9 

14.4 

9.0 

32 

9.77473 

17 

9.86  974 

27 

10.13026 

9.90499 

10 

28 

33 

9.77490 

17 

9.87000 

26 

10.13000 

9.90490 

9 

27 

34 

9.77  507 

17 

9.87027 

27 

10.12973 

9.90480 

10 

26 

9 

35 

9.77  524 

17 

9.87053 

26 

10.12947 

9.90471 

9 

25 

2    1.8 

36 

9.77541 

17 

9.87079 

26 

10.12921 

9.90462 

9 

24 

3    2.7 

37 

9.77558 

17 

9.87  106 

27 

10.12894 

9.90452 

10 

23 

4    3.6 

38 

9.77575 

17 

9.87  132 

26 

10.12868 

9.90443 

9 

22 

5    4.5 

39 

9.77592 

17 

9.87  158 

26 

10.12  842 

9.90434 

9 

21 

6    5.4 

40 

9.77(509 

17 

9.87  185 

27 

10.12815 

9.90424 

10 

20 

7    6.3 

41 

9.77  626 

17 

9.87211 

26 

10.12789 

9.90415 

9 

19 

8    7.2 

42 

9.77643 

17 

9.87238 

27 

10.12762 

9.90405 

10 

18 

9    8.1 

43 

9.77  660 

17 

9.87264 

26 

10.12736 

9.90396 

9 

17 

44 

9.77677 

17 

9.87290 

26 

10.12710 

9.90386 

10 

16 

45 

9.77694 

17 

9.87317 

27 

10.12  683 

9.90  377 

9 

15 

From  the  top: 

46 

9.77711 

17 

9.87343 

26 

10.12657 

9.90368 

9 

14 

For360+or216°+, 

47 
48 
49 

9.77728 
9.77744 
9.77761 

17 
16 
17 

9.87369 
9.87396 
9.87422 

26 
27 
26 

10.12631 
10.12604 
10.12578 

9.90358 
9.90  349 
9.90339 

10 
9 
10 

13 
12 
11 

read  as  printed;  for 
126°+  or  306°+  read 

50 

9.77778 

17 

9.87448 

26 

10.12552 

9.90330 

9 

10 

co-function. 

51 

9.77  795 

17 

9.87475 

27 

10.12525 

9.90320 

10 

9 

52 
53 

9.77812 
9.77  829 

17 
17 

9.87501 
9.87527 

26 
26 

10.12499 
10.12473 

9.90311 
9.90301 

9 
10 

8 

7 

From  the  bottom: 

54 

9.77  846 

17 
16 

9.87  554 

27 
26 

10.12446 

9.90292 

9 
10 

6 

For  53°+  or  233°+, 

55 

56 
57 

9.77  862 
9.77  879 
9.77  896 

17 
17 

9.87580 
9.87606 
9.87  633 

26 
27 

10.12420 
10.12394 
10.12367 

9.90282 
9.90273 
9.90  263 

9 

10 

5 

4 
3 

read  as  printed  ;  for 
143°+  or  323°+,  read 

58 

9.77913 

17 

9.87659 

26 

10.12341 

9.90  254 

9 

2 

co-function. 

59 

9.77930 

17 

9.87685 

26 

10.12315 

9.90  244 

10 

1 

60 

9.77946 

16 

9.87711 

26 

10.12289 

9.90  235 

9 

0 

LCos 

d 

LCtn 

cd 

LTan 

LSin 

d 

/ 

Prop.  Pts. 

53°  —  Logarithms  of  Trigonometric  Functions 


Ill]         37°  —  Logarithms  of  Trigonometric  Functions 


83 


: 

LSin 

d 

L  Tan 

cd 

LCtn 

LCos 

d 

Prop  Pts. 

0 

9.77946 

9.87711 

10.12289 

9.90  235 

60 

1 

9.77  963 

17 

9.87738 

27 

10.12262 

9.90  225 

10 

59 

2 

9.77  980 

17 

9.87  764 

26 

10.12236 

9.90216 

9 

58 

3 

9.77997 

17 

9.87790 

26 

10.12210 

9.90206 

10 

57 

4 

9.78013 

16 
17 

9.87817 

27 
26 

10.12  183 

9.90  197 

9 
10 

56 

5 

9.78  030 

9.87  843 

10.12  157 

9.90  187 

55 

27 

26 

6 

9.78047 

17 

9.87  869 

26 

OA 

10.12131 

9.90  178 

9 

54 

2 

5.4 

5.2 

7 

9.78  063 

16 

9.87  895 

zo 

10.12  105 

9.90  168 

10 

53 

0 

8'i 

7  S. 

8 
9 

9.78  080 
9.78097 

17 

17 
16 

9.87  922 
9.87  948 

27 
26 
26 

10.12078 
10.12052 

9.90  159 
9.90  149 

9 
10 
10 

52 
51 

o 

4 
5 

.1 

10.8 
13.5 

1  .0 

10.4 
13.0 

10 

9.78113 

*.87  974 

10.12026 

9.90  139 

50 

6 

16.2 

15.6 

11 

9.78130 

17 

9.88000 

26 

10.12000 

9.90  130 

9 

49 

7 

18.9 

18.2 

12 

9.78  147 

17 

9.88027 

27 

10.11973 

9.90  120 

10 

48 

8 

21.6 

20.8 

13 

9.78  163 

16 

9.88053 

26 

10.11  947 

9.90111 

9 

47 

9 

24.3 

23.4 

14 

9.78  180 

17 

9.88079 

26 

10.11921 

9.90  101 

10 

46 

15 

9.78  197 

17 

9.88  105 

26 

10.11  895 

9.90  091 

10 

45 

16 

9.78213 

16 

9.88  131 

26 

10.11869 

9.90082 

9 

44 

17 

1ft 

17 

9.78230 

17 

9.88  158 

27 

10.11842 

9.90072 

10 

43 

Jtl 

J.O 

18 

9.78246 

16 

9.88  184 

26 

10.11816 

9.90  063 

9 

43 

2 

3.4 

3.2 

19 

9.78263 

17 

1  7 

9.88210 

26 

10.11790 

9.90053 

10 

1  C\ 

41 

3 

5.1 

A  Q 

4.8 

/;    j 

20 

9.78  280 

it 

9.88236 

10.11764 

9.90043 

iv 

40 

5 

O.8 

8.5 

O.4 

Q  O 

21 

9.78296 

16 

9.88262 

26 

10.11738 

9.90  034 

9 

39 

<J,\J 
Q  A 

22 

9.78313 

17 

9.88  289 

27 

10.11711 

9.90  024 

10 

38 

7 

11.9 

y.o 
11.2 

23 

9.78329 

16 

9.88315 

26 

10.11685 

9.90  014 

10 

37 

g 

12  R 

24 

9.78346 

17 
16 

9.88341 

26 
26 

10.11  659 

9.90005 

9 
10 

36 

9 

15.3 

X^t.O 

14.4 

25 

9.78  362 

9.88367 

10.11633 

9.89  995 

35 

26 

9.78379 

17 

9.88393 

26 

10.11607 

9.89  985 

10 

34 

27 

9.78395 

16 

9.88420 

27 

10.11580 

9.89  976 

9 

33 

28 

9.78412 

17 

9.88446 

26 

10.11554 

9.89  966 

10 

32 

1U 

9 

29 

9.78428 

16 

9.88472 

26 

10.11528 

9.89  956 

10 

31 

2 

2.0 

1.8 

30 

9.78445 

17 

9.88498 

26 

10.11  502 

9.89  947 

9 

30 

3 

3.0 

2.7 

31 

9.78461 

16 

9.88  524 

26 

10.11476 

9.89  937 

10 

"O 

4 

4.0 

3.6 

32 

9.78478 

17 

9.88550 

26 

10.11450 

9.89  927 

10 

28 

5 

5.0 

4.5 

33 

9.78494 

16 

9.88577 

27 

10.11423 

9.89918 

9 

27 

6 

6.0 

5.4 

34 

9.78510 

16 

9.88  603 

26 

10.11397 

9.89  908 

10 

26 

7 

7.0 

6.3 

17 

26 

10 

8  ft 

7  9 

35 

9.78  527 

9.88  629 

10.11371 

9.89  898 

25 

9 

o.u 

9.0 

»  .— 
Q   1 

36 

9.78543 

16 

9.88  655 

M 

10.11345 

9.89  888 

10 

24 

O.  i 

37 

9.78560 

17 

9.88681 

26 

10.11319 

9.89  879 

9 

23 

38 

9.78576 

16 

9.88707 

26 

10.11293 

9.89  869 

10 

22 

39 

9.78592 

16 

9.88  733 

26 

10.11267 

9.89  859 

10 

21 

40 

9.78  609 

17 

9.88  759 

26 

10.11241 

9.89  849 

10 

20 

41 

9.78  625 

16 

9.88786 

27 

10.11214 

9.89  840 

9 

19 

42 

9.78642 

17 

9.88812 

26 

10.11  188 

9.89  830 

10 

18 

From  the  top: 

43 
44 

9.78658 
9.78674 

16 
16 

9.88  838 
9.88  864 

26 
26 

10.11  162 
10.11  136 

9.89  820 
9.89810 

10 
10 

17 
16 

For37°+or217c+, 

45 

9.78691 

17 

9.88  890 

26 

10.11110 

9.89  801« 

9 

15 

read  as  printed;  for 

46 

9.78707 

16 

9.88916 

26 

10.11084 

9.89791 

10 

14 

1270"1-  or  307°+  read 

47 

9^78723 

16 

9.88  942 

26 

10.11058 

9.89781 

10 

13 

co-function. 

4S 

9778739 

16 

9.88968 

26 

10.11032 

9.89771 

10 

12 

49 
50 

9.78756 
9.78772 

17 
16 

9.88994 
9.89  020 

26 
26 

10.11006 
10.10980 

9.89  761 
9.89  752 

10 
9 

11 
10 

From  the  bottom: 

51 

9.78788 

16 

9.89  046 

26 

10.10954 

9.89  742 

10 

9 

For52°-f-or232°-(-, 

52 
53 
54 

9.78805 
9.78821 
9.78837 

17 
16 
16 

9.89  073 
9.89  099 
9.89  125 

27 
26 
26 

10.10927 
10.10901 
10.10875 

9.89732 
9.89  722 
9.89712 

10 
10 
10 

8 
7 
6 

read  as  printed  ;  for 
142°+  or  3220-1-,  read 

55 

9.78853 

16 

9.89  151 

26 

10.10849 

9.89  702 

10 

5 

co-function. 

56 

9.78869 

16 

9.89  177 

26 

10.10823 

9.89  693 

9 

4 

57 

9.78  886 

17 

9.89  203 

26 

10.10797 

9.89  683 

10 

3 

58 

9.78902 

16 

9.89  229 

26 

10.10771 

9.89  673 

10 

2 

59 

9.78918 

16 

9.89  255 

26 

10.10745 

9.89  663 

10 

1 

60 

9.78  934 

16 

9.89  281 

26 

10.10719 

9.89  653 

10 

0 

L  Cos 

d 

LCtn 

cd 

LTan 

LSin 

d 

' 

Prop.  Pts. 

52°  —  Logarithms  of  Trigonometric  Functions 


84 


38°  —  Logarithms  of  Trigonometric  Functions          [III 


1 

LSin 

d 

LTan 

cd 

L  Ctn 

LCos 

d 

Prop.  Pts. 

0 

9.78  934 

9.89  281 

10.10719 

9.89  653 

60 

1 

9.78  950 

16 

9.89  307 

26 

10.10693 

9.89  643 

10 

59 

2 

9.78967 

17 

9.89  333 

26 

10.10667 

9.89  633 

10 

58 

26 

25 

3 

9.78  983 

16 

9.89  359 

26 

10.10641 

9.89  624 

9 

57 

2 

5  2 

5.0 

4 

9.78999 

16 
16 

9.89  385 

26 
26 

10.10615 

9.89  614 

10 
10 

56 

3 

7.8 

7.5 

5 

9.79  015 

9.89411 

10.10589 

9.89  604 

55 

4 

10.4 

10.0 

6 

9.79031 

16 

9.89  437 

26 

10.10563 

9.89  594 

10 

54 

5 

13.0 

12.5 

7 

9.79  047 

16 

9.89463 

26 

10.10537 

9.89  584 

10 

53 

6 

15.6 

15.0 

8 

9.79  063 

16 

9.89489 

26 

10.10511 

9.89  574 

10 

52 

7 

18.2 

17.5 

9 

9.79  079 

16 

9.89515 

26 

10.10485 

9.89  564, 

10 

51 

8 

20.8 

20.0 

10 

9.79  095 

16 

9.89541 

26 

10.10459 

9.89  554 

10 

50 

9 

23.4 

22.5 

11 

9.79111 

16 

9.89  567 

26 

10.10433 

9.89  544 

10 

49 

12 

9.79  128 

17 

9.89  593 

26 

10.10407 

9.89  534 

10 

48 

-«  rr               •*  ft 

13 

9.79  144 

16 

9.89619 

26 

10.10381 

9.89  524 

10 

47 

17 

ID 

14 

9.79  160 

16 

9.89  645 

26 

10.10355 

9.89514 

10 

46 

2 

3.4 

3.2 

15 

9.79  176 

16 

9.89  671 

26 

10.10329 

9.89  504 

10 

45 

3 

5.1 

4.8 

16 

9.79  192 

16 

9.89  697 

26 

10.10303 

9.89  495 

9 

44 

4 

6.8 

6.4 

17 

9.79  208 

16 

9.89  723 

26 

10.10277 

9.89485 

10 

43 

5 

8.5 

8.0 

18 

9.79  224 

16 

9.89  749 

26 

10.10251 

9.89475 

10 

42 

6 

10.2 

9.6 

19 

9.79  240 

16 

9.89  775 

26 

10.10225 

9.89465 

10 

41 

7 

11.9 

11.2 

16 

26 

10 

8 

13.6 

12.8 

20 

9.79  256 

9.89  801 

10.10  199 

9.89455 

40 

9 

15.3 

14.4 

21 

9.79  272 

16 

9.89  827 

26 

10.10  173 

9.89  445 

10 

39 

22 

9.79  288 

16 

9.89  853 

26 

10.10  147 

9.89  435 

10 

38 

23 

9.79  304 

16 

9.89  879 

26 

10.10121 

9.89  425 

10 

37 

15 

11 

24 

9.79319 

15 

16 

9.89  905 

26 
26 

10.10095 

9.89415 

10 
10 

36 

2 

3.0 

25 

9.79  335 

9.89931 

10.10069 

9.89  405 

35 

3 

4.5 

3.3 

26 

9.79351 

16 

9.89  957 

26 

10.10043 

9.89  395 

10 

34 

4 

6.0 

4.4 

27 

9.79  367 

16 

9.89  983. 

26 

10.10017 

9.89  385 

10 

33 

5 

7.5 

5.5 

28 

9.79  383 

16 

9.90009 

26 

10.09991 

9.89375 

10 

32 

6 

9.0 

6.6 

29 

9.79  399 

16 
16 

9.90035 

26 
26 

10.09  965 

9.89  364 

11 
10 

31 

7 

10.5 

7.7 

30 

9.79  415 

9.90  061 

10.09  939 

9.89  354 

30 

8 

12.0 

8.8 

31 

9.79431 

16 

9.90  086 

25 

10.09914 

9.89  344 

10 

29 

g 

13.5 

9.9 

32 

9.79  447 

16 

9.90112 

26 

10.09  888 

9.89  334 

10 

28 

33 

9.79  463 

16 

9.90138 

26 

10.09  862 

9.89  324 

10 

27 

34 

9.79478 

15 

9.90  164 

26 

10.09  836 

9.89314 

10 

26 

10 

9 

35 

9.79  494 

16 

9.90  190 

26 

10.09810 

9.89  304 

10 

25 

2 

2.0 

1.8 

36 

9.79  510 

16 

9.90216 

26 

10.09784 

9.89  294 

10 

24 

3 

3.0 

2.7 

37 

9.79  526 

16 

9.90  242 

26 

10.09758 

9.89  284 

10 

23 

4 

4.0 

3.6 

38 

9.79  542 

16 

9.90  268 

26 

10.09732 

9.89  274 

10 

22 

5 

5.0 

4.5 

39 

9.79  558 

16 

9.90294 

26 

10.09  706 

9.89  264 

10 

21 

6 

6.0 

5.4 

15 

26 

10 

•7  n 

A  ** 

40 

9.79  573 

9.90320 

10.09  680 

9.89  254 

20 

/  .u 

O    A 

O.O 

*f   O 

41 

9.79  589 

16 

9.90346 

26 

10.09  654 

9.89  244 

10 

19 

8.0 

7.2 

81 

42 

9.79  605 

16 

9.90371 

25 

10.09  629 

9.89  233 

11 

18 

9 

9.0 

.1 

43 

9.79  621 

16 

9.90397 

26 

10.09  603 

9.89  223 

10 

17 

44 
45 

9.79  636 
9.79  652 

15 
16 

9.90423 
9.90449 

26 
26 

10.09577 
10.09551 

9.89213 
9.89  203 

10 
10 

16 
15 

From  the  top: 

46 

9.79  668 

16 

9.90475 

26 

10.09  525 

9.89  193 

10 

14 

For38°+or2180+, 

47 
48 
49 

9.79  684 
9.79  699 
9.79715 

16 
15 
16 

9.90501 
9.90527 
9.90553 

26 
26 
26 

10.09499 
10.09473 
10.09447 

9.89  183 
9.89  173 
9.89  162 

10 
10 

11 

13 
12 
11 

read  as  printed  ;  for 
128°+  or  308°+  read 

50 

9.79  731 

16 

9.90578 

25 

10.09  422 

9.89  152 

10 

10 

co-function. 

51 

9.79  746 

15 

9.90604 

26 

10.09  396 

9.89  142 

10 

9 

52 
53 

9.79  762 
9.79778 

16 
16 

9.90630 
9.90  656 

26 
26 

10.09  370 
10.09  344 

9.89  132 
9.89  122 

10 
10 

8 

7 

From  the  bottom: 

54 

9.79  793 

15 
16 

9.90  682 

26 
26 

10.09318 

9.89112 

10 
11 

6 

For  SI0*  or  231°+, 

55 

56 
57 

9.79  809 
9.79  825 
9.79  840 

16 
15 

9.90708 
9.90  734 
9.90759 

26 

25 

10.09  292 
10.09  266 
10.09  241 

9.89  101 
9.89091 
9.89081 

10 
10 

5 

4 
3 

read  as  printed  ;  for 
141°+  or  321°+,  read 

58 

9.79  856 

16 

9.90785 

26 

10.09215 

9.89071 

10 

2 

co-function. 

59 

9.79  872 

16 

9.90811 

26 

10.09  189 

9.89  060 

11 

1 

60 

9.79  887 

15 

9.90837 

26 

10.09  163 

9.89  050 

10 

0 

LCos 

d 

LCtn 

cd 

L  Tan 

LSin 

d 

' 

Prop.  Pts. 

51°  —  Logarithms  of  Trigonometric  Functions 


[Ill          39°  —  Logarithms  of  Trigonometric  Functions 


85 


/ 

LSin 

d 

L  Tan 

cd 

L  Ctn 

L  Cos 

d 

Prop.  Pts. 

0 

9.79  887 

9.90837 

10.09  163 

9.89  050 

60 

1 

9.79903 

16 

9.90  863 

26 

10.09  137 

9.89  040 

10 

59 

2 

9.79918 

15 

9.90889 

26 

10.09111 

9.89  030 

10 

58 

3 

9.79934 

16 

9.90914 

25 

10.09  086 

9.89  020 

10 

57 

4 

9.79  950 

16 
15 

9.90940 

26 
26 

10.09  060 

9.89  009 

11 
10 

56 

5 

9.79965 

9.90966 

10.09  034 

9.88  999 

55 

26 

25 

6 

9.79981 

16 

9.90992 

26 

10.09  008 

9.88  989 

10 

54 

2 

5.2 

5.0 

7 

9.79996 

15 

9.91018 

26 

10.08982 

9.88978 

11 

53 

7  8 

7  £ 

8 
9 

9.80012 
9.80027 

16 
15 
16 

9.91043 
9.91  069 

25 
26 
26 

10.08957 
10.08931 

9.88968 
9.88958 

10 

10 
10 

52 
51 

4 
5 

/  .0 

10.4 
13.0 

/  .O 

10.0 
12.5 

10 

9.80043 

9.91095 

10.08  905 

9.88  948 

50 

6 

15.6 

15.0 

11 

9.80058 

15 

9.91  121 

26 

10.08  879 

9.88937 

11 

49 

7 

18.2 

17.5 

12 

9.80074 

16 

9.91  147 

26 

10.08853 

9.88927 

10 

48 

8 

20.8 

20.0 

13 

9.80089 

15 

9.91  172 

25 

10.08828 

9.88917 

10 

47 

9 

23.4 

22.5 

14 

9.80  105 

16 

9.91  198 

26 

10.08802 

9.88  906 

11 

46 

15 

26 

10 

15 

9.80  120 

9.91  224 

10.08  776 

9.88  896 

45 

16 

9.80  136 

16 

9.91250 

26 

10.08750 

9.88  886 

10 

44 

tfi 

IK 

17 

9.80151 

15 

9.91  276 

26 

10.08  724 

9.88875 

11 

43 

ID 

Ut 

18 

9.80  166 

15 

9.91301 

25 

10.08699 

9.88  865 

10 

42 

2 

3.2 

3.0 

19 

9.80182 

16 

9.91327 

26 

10.08673 

9.88  855 

10 

41 

3 

4.8 

4.5 

20 

9.80  197 

15 

9.91353 

26 

10.08647 

9.88  844 

11 

40 

4 
5 

6.4 
8.0 

6.0 
7  *> 

21 

9.80213 

16 

9.91379 

26 

10.08621 

9.88  834 

10 

39 

6 

0  ti 

i  *i> 
q  n 

22 
23 
24 

9.80228 
9.80244 
9.80259 

15 
16 
15 
15 

9.91  4Q4 
9.91430 
9.91456 

25 
26 
26 
26 

10.08596 
10.08570 
10.08  544 

9.88  824 
9.88813 
9.88803 

10 

11 

10 
10 

38 
37 
36 

7 
8 
9 

j.\j 
11.2 

12.8 
14.4 

<J*\J 

10.5 
12.0 
13.5 

25 

9.80  274 

9.91482 

10.08518 

9.88  793 

35 

26 

9.80  290 

16 

9.91507 

25 

10.08493 

9.88  782 

11 

34 

27 

9.80305 

15 

9.91533 

26 

10.08467 

9.88772 

10 

33 

28 

9.80320 

15 

9.91559 

26 

10.08441 

9.88761 

11 

32 

11 

10 

29 

9.80336 

16 

9.91  585 

26 

10.08415 

9.88751 

10 

31 

2 

2.2 

2.0 

30 

9.80351 

15 

9.91610 

25 

10.08390 

9.88741 

10 

30 

3 

3.3 

3.0 

31 

9.80366 

15 

9.91636 

26 

10.08364 

9.88730 

11 

29 

4 

4.4 

4.0 

32 

9.80382 

16 

9.91  662 

26 

10.08338 

9.88720 

10 

28 

5 

5.5 

5.0 

33 

9.80397 

15 

9.91688 

26 

10.08312 

9.88709 

11 

27 

6 

6.6 

6.0 

34 

9.80412 

15 

9.91713 

25 

10.08287 

9.88  699 

10 

26 

7 

7.7 

7.0 

16 

26 

1  1 

K  R 

ft  n 

35 

9.80428 

9.91739 

10.08261 

9.88  688 

25 

o.o 
o  n 

o.u 

f\  f\ 

36 

9.80  443 

15 

9.91765 

26 

10.08235 

9.88678 

10 

24 

y.y 

y.O 

37 

9.80458 

15 

9.91791 

26 

10.08209 

9.88668 

10 

23 

38 

9.80473 

15 

9.91816 

25 

10.08  184 

9.88  657 

11 

22 

39 

9.80  489 

16 

9.91842 

26 

10.08  158 

9.88  647 

10 

21 

40 

9.80  504 

15 

9.91  868 

26 

10.08  132 

9.88  636 

11 

20 

41 

9.80519 

15 

9.91  893 

25 

10.08107 

9.88626 

10 

19 

42 

9.80  534 

15 

9.91919 

26 

10.08081 

9.88615 

11 

18 

From  the  top: 

43 
44 

9.80550 
9.80  565 

16 
15 

9.91945 
9.91971 

26 

26 

10.08055 
10.08  029 

9.88605 
9.88  594 

10 

11 

17 
16 

For  39°+  or  219°+, 

45 

9.80  580 

15 

9.91  996 

25 

10.08  004 

9.88  584 

10 

15 

read  as  printed  ;  for 

46 

9.80  595 

15 

9.92022 

26 

10.07  978 

9.88  573 

11 

14 

129°+  or  309°+,  read 

47 

9.80610 

15 

9.92048 

26 

10.07  952 

9.88563 

10 

13 

co-function. 

48 

9.80  625 

15 

9.92073 

25 

10.07  927 

9.88552 

11 

12 

49 

9.80641 

16 

9.92  099 

26 

10.07901 

9.88  542 

10 

11 

50 

9.80  656 

15 

9.92  125 

26 

10.07  875 

9.88531 

11 

10 

From  the  bottom: 

51 

9.80671 

15 

9.92  150 

25 

10.07  850 

9.88521 

10 

9 

For50°-|-or2300-1-, 

52 
53 
54 

9.80  686 
9.80701 
9.80716 

15 
15 
15 

9.92  176 
9.92  202 
9.92  227 

26 
26 
25 

10.07  824 
10.07798 
10.07  773 

9.88510 
9.88499 
9.88489 

1  1 

11 

10 

8 
7 
6 

read  as  printed  ;  for 
140°+  or  320°+,  read 

55 

9.80731 

15 

9.92  253 

26 

10.07  747 

9.88478 

11 

5 

co-function. 

56 

9.80  746 

15 

9.92279 

26 

10.07721 

9.88468 

10 

4 

57 

9.80  762 

16 

9.92304 

25 

10.07696 

9.88457 

11 

3 

58 

9.80777 

15 

9.92330 

26 

10.07670 

9.88447 

10 

2 

59 

9.80792 

15 

9.92356 

26 

10.07  644 

9.88  436 

11 

1 

60 

9.80  807 

15 

9.92381 

25 

10.07619 

9.88  425 

11 

0 

L  Cos 

d 

L  Ctn 

cd 

LTan 

LSin 

d 

' 

Prop.  Pts. 

50°  —  Logarithms  of  Trigonometric  Functions 


86 


40°  —  Logarithms  of  Trigonometric  Functions          [III 


' 

LSin 

d 

L  Tan 

cd 

L  Ctn 

LCos 

d 

Prop.  Pts. 

0 

9.80807 

9.92381 

10.07619 

9.88425 

60 

1 

9.80822 

15 

9.92407 

26 

10.07593 

9.88415 

10 

59 

2 

9.80837 

15 

9.92433 

26 

10.07567 

9.88404 

11 

58 

3 

9.80852 

15 

9.92458 

25 

10.07542 

9.88394 

10 

57 

4 

9.80867 

15 
15 

9.92484 

26 
26 

10.07516 

9.88  383 

11 

56 

5 

9.80882 

9.92  510 

10.07490 

9.88  372 

55 

26 

25 

6 

9.80897 

15 

9.92535 

25 

10.07465 

9.88362 

10 

54 

50 

e  A 

7 

9.80912 

15 

9.92561 

26 

10.07439 

9.88351 

11 

53 

./, 

*7    O 

O.U 

7r 

8 
9 

9.80927 
9.80  942 

15 
15 
15 

9.92  587 
9.92  612 

26 
25 
26 

10.07413 
10.07  388 

9.88  340 
9.88330 

11 

10 

52 
51 

4 
5 

7.8 
10.4 
13.0 

.5 

10.0 
12.5 

10 

9.80957 

9.92638 

10.07  362 

9.88319 

50 

6 

15.6 

15.0 

11 

9.80972 

15 

9.92  663 

25 

10.07337 

9.88308 

11 

49 

7 

18.2 

17.5 

12 

9.80987 

15 

9.92  689 

26 

10.07311 

9.88298 

10 

48 

8 

20.8 

20.0 

13 

9.81  002 

15 

9.92715 

26 

10.07  285 

9.88287 

11 

47 

9 

23.4 

22.5 

14 

9.81017 

15 

9.92740 

25 

10.07  260 

9.88276 

11 

46 

15 

9.81  032 

15 

9.92766 

26 

10.07  234 

9.88266 

10 

45 

16 

9.81  047 

15 

9.92  792 

26 

10.07  208 

9.88255 

11 

44 

•1C 

14 

17 

9.81  061 

14 

9.92817 

25 

10.07  183 

9.88  244 

11 

43 

JLO 

JM 

18 

9.81  076 

15 

9.92  843 

26 

10.07  157 

9.88234 

10 

42 

2 

3.0 

2.8 

19 

9.81  091 

15 

9.92  868 

25 

10.07  132 

9.88223 

11 

41 

3 

4.5 

4.2 

20 

21 

9.81  106 
9.81  121 

15 
15 

9.92  894 
9.92  920 

26 
26 

10.07  106 
10.07080 

9.88212 
9.88201 

11 

11 

40 

39 

4 
5 

6.0 
7.5 

O  A 

5.6 
7.0 

ft  A. 

22 

9.81  136 

15 

9.92  945 

25 

10.07055 

9.88  191 

10 

38 

y.u 

1  f\    K 

o.*r 

23 

9.81  151 

15 

9.92971 

26 

10.07029 

9.88  180 

11 

37 

l(J.O 
°l  O  A 

9.8 

1  1     O 

24 

9.81  166 

15 
14 

9.92  996 

25 
26 

10.07004 

9.88  169 

11 

11 

36 

9 

l^.U 

13.5 

12.6 

25 

9.81  180 

9.93  022 

10.06978 

9.88  158 

35 

26 

9.81  195 

15 

9.93  048 

26 

10.06952 

9.88  148 

10 

34 

27 

9.81  210 

15 

9.93  073 

25 

10.06  927 

9.88  137 

11 

33 

28 

9.81  225 

15 

9.93  099 

26 

10.06901 

9.88  126 

11 

32 

11 

IP 

29 

9.81  240 

15 

9.93  124 

25 

10.06  876 

9.88  115 

11 

31 

2 

2.2 

2.0 

30 

9.81  254 

14 

9.93  150 

26 

10.06  850 

9.88  105 

10 

30 

3 

3.3 

3.0 

31 

9.81  269 

15 

9.93  175 

25 

10.06  825 

9.88094 

11 

29 

4 

4.4 

4.0 

32 

9.81  284 

15 

9.93  201 

26 

10.06799 

9.88  083 

11 

28 

5 

5.5 

5.0 

33 

9.81  299 

15 

9.93  227 

26 

10.06773 

9.88072 

11 

27 

6 

6.6 

6.0 

34 

9.81314 

15 

9.93  252 

25 

10.06  748 

9.88061 

11 

26 

7 

7.7 

7.0 

14 

26 

10 

a  Q 

ft  n 

35 

9.81  328 

9.93  278 

10.06722 

9.88051 

25 

o.o 

O   A 

o.ly 
CL  f\ 

36 

9.81  343 

15 

9.93  303 

25 

10.06697 

9.88  040 

11 

24 

9.9 

9.U 

37 

9.81  358 

15 

9.93  329 

26 

10.06671 

9.88  029 

11 

23 

38 

9.81  372 

14 

9.93  354 

25 

10.06  646 

9.88018 

11 

22 

39 

9.81  387 

15 

9.93  380 

26 

10.06  620 

9.88  007 

11 

21 

40 

9.81  402 

15 

9.93406 

26 

10.06  594 

9.87  996 

11 

20 

41 

9.81  41Z 

15 

9.93431 

25 

10.06569 

9.87  985 

11 

19 

42 

9.81431 

14 

9.93457 

26 

10.06543 

9.87  975 

10 

18 

From  the  top: 

43 
44 

9.81  446 
9.81461 

15 
15 

9.93  482 
9.93  508 

25 
26 

10.06518 
10.06492 

9.87  964 
9.87953 

11 

11 

17 
16 

For  40°+  or  220°+ 

45 

9.81  475 

14 

9.93  533 

25 

10.06467 

9.87  942 

11 

15 

read  as  printed;  for 

46 

9.81  490 

15 

9.93  559 

26 

10.06441 

9.87931 

11 

14 

130°+  or  310°+  read 

47 

9.81  505 

15 

9.93  584 

25 

10.06416 

9.87920 

11 

13 

co-function. 

48 

9.81519 

14 

9.93  610 

26 

10.06390 

9.87909 

11 

12 

49 

9.81  534 

15 

9.93  636 

26 

10.06364 

9.87  898 

11 

11 

50 

9.81  549 

15 

9.93  661 

25 

10.06  339 

9.87  887 

11 

10 

From  the  bottom: 

51 

9.81  563 

14 

9.93  687 

26 

10.06313 

9.87  877 

10 

9 

For49°-|-or2290+, 

52 

53 
54 

9.81  578 
9.81  592 
9.81  607 

15 
14 
15 

9.93712 
9.93  738 
9.93  763 

25 
26 
25 

10.06  288 
10.06262 
10.06237 

9.87866 
9.87855 
9.87  844 

11 

11 
11 

8 
7 
6 

read  as  printed  ;  for 
139°+  or  319°+,  read 

55 

9.81  622 

15 

9.93  789 

26 

10.06211 

9.87  833 

11 

5 

co-function. 

56 

9.81  636 

14 

9.93814 

25 

10.06  186 

9.87  822 

11 

4 

57 

9.81  651 

15 

9.93  840 

26 

10.06  160 

9.87811 

11 

3 

58 

9.81  665 

14 

9.93  865 

25 

10.06  135 

9.87  800 

11 

2 

59 

9.81  680 

15 

9.93  891 

26 

10.06  109 

9.87  789 

11 

1 

60 

9.81  694 

14 

9.93916 

25 

10.06084 

9.87  778 

11 

0 

LCos 

d 

L  Ctn 

cd 

L  Tan 

LSin 

d 

' 

Prop.  Pts. 

49°  —  Logarithms  of  Trigonometric  Functions 


Ill]         41°  —  Logarithms  of  Trigonometric  Functions 


87 


/ 

LSin 

d 

LTan 

cd 

L  Ctn 

LCos 

d 

Prop.  Pts. 

0 

9.81  694 

9.93916 

10.06  084 

9.87  778 

60 

1 

9.81  709 

15 

9.93  942 

26 

10.06058 

9.87  767 

ll 

59 

2 

9.81  723 

14 

9.93967 

25 

10.06033 

9.87756 

11 

58 

3 

9.81  738 

15 

9.93  993 

26 

10.06007 

9.87745 

11 

57 

4 

9.81  752 

14 

9.94018 

25 

10.05  982 

9.87734 

11 

56 

5 

9.81  767 

15 

9.94044 

26 

10.05956 

9.87723 

l] 

55 

26 

25 

6 

9.81781 

14 

9.94069 

25 

10.05931 

9.87712 

ll 

54 

2 

5.2 

5.0 

7 

9.81  796 

15 

9.94  095 

26 

10.05905 

9.87701 

11 

53 

3 

7~.8 

7^5 

8 

9.81810 

14 

9.94  120 

25 

10.05  880 

9.87690 

11 

52 

4 

10.4 

10.0 

9 

9.81  825 

15 
14 

9.94  146 

26 
25 

10.05  854 

9.87  679 

ll 

51 

5 

13.0 

12.5 

10 

9.81  839 

9.94  171 

10.05  829 

9.87  668 

50 

6 

15.6 

15.0 

11 

9.81  854 

15 

9.94  197 

26 

10.05  803 

9.87  657 

ll 

49 

7 

18.2 

17.5 

12 

9.81  868 

14 

9.94222 

25 

10.05778 

9.87  646 

11 

48 

8 

20.8 

20.0 

13 

9.81  882 

14 

9.94  248 

26 

10.05752 

9.87635 

11 

47 

9 

23.4 

22.5 

14 

9.81  897 

15 
14 

9.94273 

25 
26 

10.05  727 

9.87624 

11 
11 

46 

15 

9.81911 

9.94299 

10.05  701 

9.87  613 

45 

16 

9.81  926 

15 

9.94324 

25 

10.05676 

9.87601 

12 

44 

15 

14 

17 

9.81  940 

14 

9.94350 

26 

10.05  650 

9.87590 

11 

43 

mim 

vu 

18 

9.81  955 

15 

9.94375 

25 

10.05  625 

0.87579 

11 

42 

2 

3.0 

2.8 

19 

9.81  969 

14 

9.94401 

26 

10.05599 

9.87  568 

11 

41 

3 

4.5 

4.2 

14 

25 

11 

4 

6.0 

5.6 

20 

9.81  983 

9.94426 

10.05  574 

9.87557 

40 

5 

7^5 

7.0 

21 

9.81  998 

15 

9.94452 

26 

10.05  548 

9.87546 

11 

39 

6 

9!o 

c  4 

22 

9.82012 

14 

9.94477 

25 

10.05523 

9.87535 

11 

38 

7 

10.5 

O.T± 

9.8 

23 

9.82  026 

14 

9.94503 

26 

10.05497 

9.87524 

11 

37 

g 

12.0 

n'o 

24 

9.82041 

15 
14 

9.94528 

25 
26 

10.05472 

9.87513 

11 
12 

36 

9 

13.5 

»M 

12.6 

25 

9.82  055 

9.94554 

10.05446 

9.87501 

35 

26 

9.82069 

14 

9.94579 

25 

10.05421 

9.87490 

11 

34 

27 

9.82  084 

15 

&.94  604 

25 

10.05  396 

9.87479 

11 

33 

28 

9.82  098 

14 

9.94  630 

26 

10.05370 

9.87468 

11 

32 

12 

11 

29 

9.82112 

14 

9.94655 

25 

10.05  345 

9.87457 

11 

31 

2 

2.4 

2.2 

30 

9.82  126 

14 

9.94  681 

26 

10.05319 

9.87446 

11 

30 

3 

3.6 

3.3 

31 

9.82141 

15 

9.94  706 

25 

10.05  294 

9.87434 

12 

29 

4 

4.8 

4.4 

32 

9.82  155 

14 

9.94732 

26 

10.05268 

9.87423 

11 

28 

5 

6.0 

5.5 

33 

9.82  169 

14 

9.94757 

25 

10.05243 

9.87412 

11 

27 

6 

7.2 

6.6 

34 

9.82  184 

15 

9.94783 

26 

2r 

10.05  217 

9.87401 

11 

26 

7 

8.4 
f\  r» 

7.7 

o  o 

35 

36 

9.82  198 
9.82212 

14 

9.94808 
9.94834 

0 

26 

10.05  192 
10.05  166 

9.87390 
9.87  378 

12 

25 

24 

9 

9.6 
10.8 

8.8 
9.9 

37 

9.82  226 

14 

9.94859 

25 

10.05  141 

9.87  367 

11 

23 

38 

9.82  240 

14 

9.94884 

25 

10.05116 

9.87356 

11 

22 

39 

9.82  255 

15 

9.94910 

26 

10.05  090 

9.87  345 

11 

21 

40 

9.82  269 

14 

9.94935 

25 

10.05  065 

9.87334 

11 

20 

41 

9.82  283 

14 

9.94961 

26 

10.05  039 

9.87322 

12 

19 

42 

9.82297 

14 

9.94  986 

25 

10.05  014 

9.87311 

11 

18 

From  the  top: 

43 
44 

9.82311 
9.82  326 

14 
15 

9.95012 
9.95037 

26 
25 

10.04988 
10.04963 

9.87  300 
9.87  288 

11 
12 

17 
16 

For41°+or2210+, 

45 

9.82  340 

14 

9.95  062 

25 

10.04938 

9.87277 

11 

15 

read  as  printed  ;  for 

46 

9.S2  354 

14 

9.95  088 

26 

10.04912 

9.87  266 

11 

14 

131°+  or  311°+  read 

47 

9.82  368 

14 

9.95  113 

25 

10.04887 

9.87  255 

11 

13 

co-function. 

48 

9.82  382 

14 

9.95  139 

26 

10.04861 

9.87  243 

12 

12 

49 

9.82396 

14 

9.95  164 

25 

10.04  836 

9.87  232 

11 

11 

50 

9.82410 

14 

9.95  190 

26 

10.04810 

9.87  221 

11 

10 

From  the  bottom: 

51 

9.82424 

14 

9.95215 

25 

10.04785 

9.87  209 

12 

9 

For  48°+  or  228°+, 

52 
53 
54 

9.82439 
9.82453 
9.82467 

15 
14 
14 

9.95  240 
9.95  266 
9.95291 

25 
26 
25 

10.04760 
10.04  734 
10.04709 

9.87  198 
9.87  187 
9.87  175 

11 
11 
12 

8 
7 
6 

read  as  printed  ;  for 
138°+  or  318°+  read 

55 

9.82481 

14 

9.95317 

26 

10.04683 

9.87  164 

11 

5 

co-function. 

56 

9.82  495 

14 

9.95  342 

25 

10.04658 

9.87  153 

11 

4 

57 

9.82509 

14 

9.95  368 

26 

10.04632 

9.87  141 

12 

3 

58 

9.82  523 

14 

9.95393 

25 

10.04  607 

9.87  130 

11 

2 

59 

9.82537 

14 

9.95418 

25 

10.04582 

9.87  119 

11 

1 

60 

9.82551 

14 

9.95444 

26 

10.04556 

9.87  107 

12 

0 

LCos 

d 

LCtn 

cd 

L  Tan 

LSin 

d 

/ 

Prop.  Pts. 

48°  —  Logarithms  of  Trigonometric  Functions 


88 


42°  —  Logarithms  of  Trigonometric  Functions 


[III 


1 

LSin 

d 

LTan 

cd 

LCtn 

LCos 

d 

Prop.  Pts. 

0 

9.82551 

9.95  444 

10.04  556 

9.87  107 

60 

1 

9.82565 

14 

9.95  469 

25 

10.04531 

9.87  096 

ll 

59 

2 

9.82  579 

14 

9.95495 

26 

10.04505 

9.87  085 

11 

58 

3 

9.82  593 

14 

9.95  520 

25 

10.04480 

9.87073 

12 

57 

4 

9.82  607 

14 

9.95  545 

25 

10.04455 

9.87062 

11 

56 

5 

9.82  621 

14 

9.95  571 

26 

10.04429 

9.87  050 

12 

55 

26 

25 

6 

9.82  635 

14 

9.95  596 

25 

10.04  404 

9.87039 

11 

54 

2 

5.2 

5.0 

7 

9.82  649 

14 

9.95  622 

26 

10.04378 

9.87028 

11 

53 

i-r  c 

8 
9 

9.82663 
9.82  677 

14 
14 
14 

9.95  647 
9.95  672 

25 
25 
26 

10.04  353 
10.04  328 

9.87016 
9.87  005 

12 
11 
12 

52 
51 

4 
5 

10'.4 
13.0 

7.5 
10.0 
12.5 

10 

9.82  691 

9.95  698 

10.04  302 

9.86  993 

50 

6 

15.6 

15.0 

11 

9.82  705 

14 

9.95  723 

25 

10.04  277 

9.86982 

11 

49 

7 

18.2 

17.5 

12 

9.82719 

14 

9.95  748 

25 

10.04  252 

9.86970 

12 

48 

8 

20.8 

20.0 

13 

9.82  733 

14 

9.95774 

26 

10.04  226 

9.86959 

11 

47 

9 

23.4 

22.5 

14 

9.82  747 

14 

9.95  799 

25 

10.04201 

9.86947 

12 

46 

15 

9.82  761 

14 

9.95  825 

26 

10.04  175 

9.86936 

11 

45 

16 

9.82  775 

14 

9.95  850 

25 

10.04  150 

9.86  924 

12 

44 

14. 

19 

17 

9.82  788 

13 

9.95  875 

25 

10.04  125 

9.86913 

11 

43 

14 

lo 

18 

9.82  802 

14 

9.95  901 

26 

10.04099 

9.86  902 

11 

42 

2 

2.8 

2.6 

19 

9.82816 

14 

9.95  926 

25 

10.04  074 

9.86890 

12 

41 

3 

4.2 

3.9 

20 

9.82  830 

14 

9.95  952 

26 

10.04  048 

9.86  879 

11 

40 

4 

5.6 

7  n 

5.2 

6e 

21 

9.82  844 

14 

9.95  977 

25 

10.04023 

9.86  867 

12 

39 

/.U 

Q  A 

.O 

*7  Q 

22 

9.82  858 

14 

9.96002 

25 

10.03  998 

9.86855 

12 

38 

o.4 

9Q 

7.8 

91 

23 

9.82  872 

14 

9.96  028 

26 

10.03  972 

9.86844 

11 

37 

.8 
Uo 

.1 

24 

9.82  885 

13 

14 

9.96  053 

25 
25 

10.03  947 

9.86  832 

12 
11 

36 

9 

./ 
12.6 

11.7 

25 

9.82  899 

9.96078 

10.03  922 

9.86821 

35 

26 

9.82913 

14 

9.96  104 

26 

10.03  896 

9.86  809 

12 

34 

27 

9.82  927 

14 

9.96  129 

25 

10.03871 

9.86798 

11 

33 

28 

9.82  941 

14 

9.96  155 

26 

10.03  845 

9.86786 

12 

32 

12 

11 

29 

9.82  955 

14 

9.96  180 

25 

10.03820 

9.86776 

11 

31 

2 

2.4 

2.2 

30 

9.82  968 

13 

9.96205 

25 

10.03  795 

9.86763 

12 

30 

3 

3.6 

3.3 

31 

9.82  982 

14 

9.96231 

26 

10.03769 

9.86752 

11 

29 

4 

4.8 

4.4 

32 

9.82  996 

14 

9.96  256 

25 

10.03  744 

9.86740 

12 

28 

5 

6.0 

5.5 

33 

9.83  010 

14 

9.96281 

25 

10.03719 

9.86  728 

12 

27 

6 

7.2 

6.6 

34 

9.83  023 

13 

9.96  307 

26 

10.03  693 

9.86717 

11 

26 

7 

8.4 

7.7 

14 

25 

12 

Q  ft 

R  a 

35 

9.83  037 

9.96  332 

10.03  668 

9.86705 

25 

y.o 

1  A  Q 

o.o 

O  Cl 

36 

9.83  051 

14 

9.96357 

25 

10.03  643 

9.86694 

11 

24 

lO.o 

y.y 

37 

9.83  065 

14 

9.96  383 

26 

10.03617 

9.86682 

12 

23 

38 

9.83  078 

13 

9.96408 

25 

10.03  592 

9.86670 

12 

22 

39 

9.83  092 

14 

9.96433 

25 

10.03  567 

11 

21 

40 

9.83106' 

14 

9.96459 

26 

10.03  541 

"9^86647 

12 

20 

41 

9.83  120 

14 

9.96484 

25 

10.03516 

9.86635 

12 

19 

42 

9.83  133 

13 

9.96510 

26 

10.03490 

9.86624 

11 

18 

From  the  top: 

43 
44 

9.83  147 
9.83  161 

14 
14 

9.96535 
9.96560 

25 
25 

10.03  465 
10.03  440 

9.86612 
9.86600 

12 
12 

17 
16 

For42°+or2220-|-t 

45 

9.83  174 

13 

9.96586 

26 

10.03  414 

9.86  589 

11 

15 

read  as  printed  ;  for 

46 

9.83  188 

14 

9.96611 

25 

10.03  389 

9.86577 

12 

14 

1320+or312°-t-,read 

47 

9.83  202 

14 

9.96636 

25 

10.03  364 

9.86565 

12 

13 

co-function. 

48 

9.83215 

13 

9.96662 

26 

10.03338 

9.86  554 

11 

12 

49 

9.83  229 

14 

9.96687 

25 

10.03313 

9.86542 

12 

11 

50 

9.83  242 

13 

9.96712 

25 

10.03  288 

9.86530 

12 

10 

From  the  bottom: 

51 

9.83  256 

14 

9.96738 

26 

10.03  262 

9.86518 

12 

9 

For  47°+  or  227°+ 

52 
53 
54 

9.83  270 
9.83  283 
9.83  297 

14 
13 

14 

9.96763 
9.96788 
9.96814 

25 
25 
26 

10.03  237 
10.03212 
10.03  186 

9.86507 
9.86495 
986483 

11 
12 
12 

8 
7 
6 

read  as  printed  ;  for 
137°+  or  317°+  read 

55 

9.83310 

13 

9.96839 

25 

10.03  161 

9.86472 

11 

5 

co-function. 

56 

9.83  324 

14 

9.96  864 

25 

10.03  136 

9.86460 

12 

4 

57 

9.83  338 

14 

9.96890 

26 

10.03110 

9.86448 

12 

3 

58 

9.83  351 

13 

9.96915 

25 

10.03  085 

9.86436 

12 

2 

59 

9.83  365 

14 

9.96940 

25 

10.03  060 

9.86425 

11 

1 

60 

9.83  378 

13 

9.96966 

26 

10.03  034 

9.86413 

12 

0 

LCos 

d 

LCtn 

cd 

LTan 

LSin 

d 

' 

Prop.  Pts. 

47°  —  Logarithms  of  Trigonometric  Functions 


Ill]          43°  —  Logarithms  of  Trigonometric  Functions 


89 


' 

LSin 

d 

LTan 

cd 

LCtn 

LCos 

d 

Prop.  Pts. 

0 

9.83  378 

9.96  966 

10.03  034 

9.86413 

60 

1 

9.83  392 

14 

9.96991 

25 

10.03  009 

9.86401 

12 

59 

2 

9.83  405 

13 

9.97016 

25 

10.02  984 

9.86  389 

12 

58 

3 

9.83419 

14 

9.97  042 

26 

10.02958 

9.86377 

12 

57 

4 

9.83  432 

13 

9.97  067 

25 

10.02  933 

9.86360 

11 

56 

5 

9.83  446 

14 

9.97  092 

25 

10.02  908 

9.86354 

12 

55 

26 

25 

6 

9.83  459 

13 

9.97118 

26 

10.02  882 

9.86342 

12 

54 

2 

5.2 

5.0 

7 

9.83  473 

14 

9.97  143 

25 

10.02  857 

9.86330 

12 

53 

3 

7.8 

7.5 

8 

9.83  486 

13 

9.97  168 

25 

10.02832 

9.86318 

12 

52 

4 

10.4 

10.0 

9 

9.83  500 

14 
13 

9.97  193 

25 
26 

10.02807 

9.86  306 

12 
11 

51 

5 

13.0 

12.5 

10 

9.83  513 

9.97219 

10.02  781 

9.86295 

50 

6 

15.6 

15.0 

11 

9.83  527 

14 

9.97  244 

25 

10.02756 

9.86  283 

12 

49 

7 

18.2 

17.5 

12 

9.83  540 

13 

9.97  269 

25 

10.02  731 

9.86271 

12 

48 

8 

20.8 

20.0 

13 

9.83  554 

14 

9.97  295 

26 

10.02  705 

9.86  259 

12 

47 

9 

23.4 

22.5 

14 

9.83  567 

13 

9.97  320 

25 

10.02  680 

9.86247 

12 

46 

15 

9.83  581 

14 

9.97345 

25 

10.02  655 

9.86  235 

12 

45 

16 

9.83  594 

13 

9.97371 

26 

10.02  629 

9.86223 

12 

44 

1d 

•10 

17 

9.83  608 

14 

9.97396 

25 

10.02604 

9.86211 

12 

43 

14 

-LO 

18 

9.83  621 

13 

9.97421 

25 

10.02579 

9.86  200 

11 

42 

2 

2.8 

2.6 

19 

9.83  634 

13 

9.97447 

26 

10.02553 

9.86  188 

12 

41 

3 

4.2 

3.9 

14 

25 

12 

4 

5.6 

5.2 

20 

9.83  648 

9.97472 

10.02528 

9.86  176 

40 

5 

7.0 

6.5 

21 

9.83661 

13 

9.97497 

25 

10.02503 

9.86  164 

12 

39 

6 

8.4 

7.8 

22 

9.83  674 

13 

9.97523 

26 

10.02477 

9.86  152 

12 

38 

7 

g'g 

9'.! 

23 

9.83  688 

14 

9.97548 

25 

10.02452 

9.86  140 

12 

37 

i 
g 

11*2 

10.4 

24 

9.83701 

13 
14 

9.97573 

25 
25 

10.02427 

9.86  128 

12 
12 

36 

9 

12^6 

11.7 

25 

9.83715 

9.97  598 

10.02402 

9.86  116 

35 

26 

9.83  728 

13 

9.97  624 

26 

10.02  376 

9.86  104 

12 

34 

27 

9.83  741 

13 

9.97  649 

25 

10.02351 

9.86  092 

12 

33 

28 

9.83  755 

14 

9.97  674 

25 

10.02  326 

9.86  080 

12 

32 

12 

11 

29 

9.83  768 

13 

9.97  700 

26 

10.02  300 

9.86  068 

12 

31 

2 

2.4 

2.2 

30 

9.83  781 

13 

9.97  725 

25 

10.02  275 

9.86056 

12 

30 

3 

3.6 

3.3 

31 

9.83  795 

14 

9.97750 

25 

10.02  250 

9.86044 

12 

29 

4 

4.8 

4.4 

32 

9.83  808 

13 

9.97776 

26 

10.02  224 

9.86032 

12 

28 

5 

6.0 

5.5 

33 

9.83  821 

13 

9.97801 

25 

10.02  199 

9.86  020 

12 

27 

6 

7.2 

6.6 

34 

9.83  834 

13 

9.97  826 

25 

10.02  174 

9.86  008 

12 

26 

7 

8.4 

7.7 

14 

25 

12 

ij 

Q  ft 

8  8 

35 

36 

9.83  848 
9.83  861 

13 

9.97851 
9.97  877 

26 

10.02  149 
10.02  123 

9.85  996 
9.85  984 

12 

25 

24 

9 

•?•  VJ 

10.8 

9^9 

37 

9.83  874 

13 

9.97902 

25 

10.02  098 

9.85  972 

12 

23 

38 

9.83  887 

13 

9.97927 

25 

10.02  073 

9.85  960 

12 

22 

39 

9.83901 

14 

9.97  953 

26 

10.02  047 

9.85  948 

12 

2l 

40 

9.83  914 

13 

9.97  978 

25 

10.02  022 

9.85  936 

12 

20 

41 

9.83  927 

13 

9.98003 

25 

10.01  997 

9.85  924 

12 

19 

42 

9.83  940 

13 

9.98029 

26 

10.01971 

9.85912 

12 

18 

From  the  top: 

43 
44 

9.83  954 
9.83  967 

14 
13 

9.98054 
9.98079 

25 
25 

10.01  946 
10.01921 

9.85  900 
9.85  888 

12 
12 

17 
16 

For  430-1-  or  223°+ 

45 

9.83  980 

13 

9.98  104 

25 

10.01  896 

9.85  876 

12 

15 

read  as  printed;  for 

46 

9.83  993 

13 

9.98  130 

26 

10.01870 

9.85  864 

12 

14 

1330+or3130+,read 

47 

9.84006 

13 

9.98  155 

25 

as 

10.01  845 

9.85  851 

13 

13 

co-function. 

48 

9.84020 

14 

9.98  180 

D 

10.01  820 

9.85  839 

\i 

12 

49 

9.84  033 

13 

9.98  206 

26 

10.01  794 

9.85  827 

12 

11 

50 

9.84  046 

13 

9.98231 

25 

10.01  769 

9.85  815 

12 

10 

From  the  bottom: 

51 

9.84059 

13 

9.98256 

25 

10.01  744 

9.85  803 

12 

9 

For  46°+  or  226°+ 

52 
53 
54 

9.84072 
9.84  085 
9.84098 

13 
13 

13 

9.98281 
9.98307 
9.98332 

25 
26 
25 

10.01719 
10.01  693 
10.01  668 

9.85791 
9.85  779 
9.85  766 

12 
12 
13 

8 
7 
6 

read  as  printed;  for 
1360+or316°+,read 

55 

9.84112 

14 

9.98  357 

25 

10.01  643 

9.85  754 

12 

5 

co-function. 

56 

9.84  125 

13 

9.98383 

26 

10.01617 

9.85  742 

12 

4 

57 

9.84  138 

13 

9.98408 

25 

10.01  592 

9.85  730 

12 

3 

58 

9.84  151 

13 

9.98433 

25 

10.01  567 

9.85718 

12 

2 

59 

9.84  164 

13 

9.98458 

25 

10.01  542 

9.85706 

12 

1 

60 

9.84  177 

13 

9.98484 

26 

10.01  516 

9.85  693 

13 

0 

LCos 

d 

LCtn 

cd 

L  Tan 

LSin 

d 

' 

Prop.  Pts. 

46°  —  Logarithms  of  Trigonometric  Functions 


90 


44°  —  Logarithms  of  Trigonometric  Functions 


[III 


' 

LSin 

d 

LTan 

cd 

L  Ctn 

L  Cos 

d 

Prop.  Pts. 

0 

9.84  177 

9.98484 

10.01516 

9.85  693 

60 

1 

9.84  190 

13 

9.98509 

25 

10.01491 

9.85681 

12 

59 

2 

9.84  203 

13 

9.98  534 

25 

10.01  466 

9.85  669 

12 

58 

3 

9.84216 

13 

9.98560 

26 

10.01440 

9.85  657 

12 

57 

4 

9.84  229 

13 

9.98585 

25 

10.01415 

9.85  645 

12 

56 

5 

9.84  242 

13 

9.98610 

25 

10.01  390 

9.85  632 

13 

55 

26 

25 

6 

9.84  255 

13 

9.98635 

25 

10.01365 

9.85  620 

12 

54 

2 

5.2 

5.0 

7 

9.84  269 

14 

9.98661 

26 

10.01  339 

9.85608 

12 

53 

3 

7~.8 

7.5 

8 

9.84  282 

13 

9.98686 

25 

10.01  314 

9.85  596 

12 

52 

4 

10.4 

10.0 

9 

9.84  295 

13 
13 

9.98711 

25 
26 

10.01  289 

9.85  583 

13 
12 

51 

5 

13.0 

12.5 

10 

9.84308 

9.98737 

10.01  263 

9.85571 

50 

6 

15.6 

15.0 

11 

9.84321 

13 

9.98762 

25 

10.01  238 

9.85  559 

12 

49 

7 

18.2 

17.5 

12 

9.84334 

13 

9.98  787 

25 

10.01213 

9.85  547 

12 

48 

8 

20.8 

20.0 

13 

9.84  347 

13 

9.98812 

25 

10.01  188 

9.85  534 

13 

47 

9 

23.4 

22.5 

14 

9.84  360 

13 

9.98  838 

26 

10.01  162 

9.85  522 

12 

46 

15 

9.84  373 

13 

9.98  863 

25 

10.01  137 

9.85510 

12 

45 

16 

9.84  385 

12 

9.98  888 

25 

10.01  112 

9.85  497 

13 

44 

14 

10 

17 

9.84  398 

13 

9.98913 

25 

10.01  087 

9.85  485 

12 

43 

14 

J.O 

18 

9.84411 

13 

9.98  939 

26 

10.01  061 

9.85473 

12 

42 

2 

2.8 

2.6 

19 

9.84424 

13 

9.98  964 

25 

10.01  036 

9.85460 

13 

41 

3 

4.2 

3.9 

13 

25 

12 

4 

5.6 

5.2 

20 

9.84437 

9.98  989 

10.01  Oil 

9.85  448 

40 

5 

7^0 

6.5 

21 

9.84450 

13 

9.99015 

26 

10.00  985 

9.85  436 

12 

39 

a  /i 

22 

9.84  463 

13 

9.99  040 

25 

10.00  960 

9.85  423 

13 

38 

7 

o.^t 

90 

91 

23 

9.84  476 

13 

9.99  065 

25 

10.00935 

9.85411 

12 

37 

I 

g 

.0 

11.2 

.  L 

10.4 

24 

9.84  489 

13 
13 

9.99090 

25 
26 

10.00910 

9.85  399 

12 

13 

36 

9 

11.7 

25 

9.84  502 

9.99  116 

10.00  884 

9.85  386 

35 

26 

9.84515 

13 

9.99  141 

25 

10.00  859 

9.85  374 

12 

34 

27 

9.84  528 

13 

9.99  166 

25 

10.00834 

9.85361 

13 

33 

28 

9.84  540 

12 

9.99  191 

25 

10.00  809 

9.85  349 

12 

32 

u 

29 

9.84  553 

13 

9.99  217 

26 

10.00783 

9.85  337 

12 

31 

2      2.4 

30 

9.84  566 

13 

9.99  242 

25 

10.00  758 

9.85  324 

13 

30 

3      3.6 

31 

9.84  579 

13 

9.99  267 

25 

10.00733 

9.85312 

12 

29 

4      4.8 

32 

9.84  592 

13 

9.99  293 

26 

10.00707 

9.85  299 

13 

28 

5      6.0 

33 

9.84  605 

13 

9.99318 

25 

10.00682 

9.85  287 

12 

27 

6      7.2 

34 

9.84  618 

13 

9.99  343 

25 

10.00  657 

9.85  274 

13 

26 

7      8.4 

35 

9.84  630 

12 

9.99  368 

25 

10.00  632 

9.85  262 

12 

25 

8      9.6 
91  n  ft 

36 

9.84  643 

13 

9.99  394 

26 

10.00  606 

9.85  250 

12 

24 

lUiO 

37 

9.84  656 

13 

9.99419 

25 

10.00581 

9.85  237 

13 

23 

38 

9.84  669 

13 

9.99  444 

25 

10.00556 

9.85225 

12 

22 

39 

9.84  682 

13 

9.99  469 

25 

10.00531 

9.85212 

13 

21 

40 

9.84  694 

12 

9.99  495 

26 

10.00505 

9.85  200 

12 

20 

41 

9.84  707 

13 

9.99  520 

25 

10.00480 

9.85  187 

13 

19 

42 

9.84  720 

13 

9.99  545 

25 

10.00455 

9.85  175 

12 

18 

From  the  top: 

43 
44 

9.84  733 
9.84  745 

13 

12 

9.99570 
9.99  596 

25 
26 

10.00430 
10.00404 

9.85  162 
9.85  150 

13 
12 

17 
16 

For  44°+  or  224°+, 

45 

9.84  758 

13 

9.99  621 

25 

10.00  379 

9.85  137 

13 

15 

read 

as  printed  ;  for 

46 

9.84771 

13 

9.99  646 

25 

10.00  354 

9.85  125 

12 

14 

134°+  or  314°+,  read 

47 

9.84  784 

13 

9.99672 

26 

10.00328 

9.85  112 

13 

13 

co-function. 

48 

9.84  796 

12 

9.99  697 

25 

10.00303 

9.85  100 

1- 

12 

49 

9.84  809 

13 

9.99  722 

25 

10.00  278 

9.85  087 

13 

11 

50 

9.84  822 

13 

9.99  747 

25 

10.00  253 

9.85  074 

13 

10 

From  the  bottom: 

51 

9.84  835 

13 

9.99  773 

26 

10.00227 

9.85062 

12 

9 

For450+or225°+, 

52 
53 

54 

9.84  847 
9.84860 
9.84  873 

12 
13 
13 

9.99798 
9.99  823 
9.99  848 

25 
25 
25 

10.00  202 
10.00  177 
10.00  152 

9.85  049 
9.85037 
9.85  024 

13 
12 
13 

8 
7 
6 

read  as  printed;  for 
1350+or3150+,read 

55 

9.84  885 

12 

9.99  874 

26 

10.00  126 

9.85012 

12 

5 

co-function. 

56 

9.84  898 

13 

9.99  899 

25 

10.00  101 

9.84  999 

13 

4 

57 

9.84911 

13 

9.99  924 

25 

10.00076 

9.84  986 

13 

3 

58 

9.84  923 

12 

9.99  949 

25 

10.00051 

9.84  974 

12 

2 

59 

9.84  936 

13 

9.99  975 

26 

10.00025 

9.84961 

13 

1 

60 

9.84  949 

13 

10.0000 

25 

10.00000 

9.84  949 

12 

0 

LCos 

d 

L  Ctn 

cd 

LTan 

LSin 

d 

' 

Prop.  Pts. 

45°  —  Logarithms  of  Trigonometric  Functions 


IV]  Table  IV  —  Degrees,  Minutes,  and  Seconds  to  Radians   91 


Degrees 

Minutes 

Seconds 

0° 

0.00000  00 

60° 

1.04719  76 

120° 

2.0943951 

0 

0.00000  00 

0 

0.00000  00 

1 

0.01745  33 

61 

1.06465  08 

121 

2.1118484 

l 

0.00029  09 

1 

0.00000  48 

2 

0.03490  66 

62 

1.0821041 

122 

2.12930  17 

2 

0.00058  18 

2 

0.00000  97 

3 

0.05235  99 

63 

1.09955  74 

123 

2.14675  50 

3 

0.00087  27 

3 

0.00001  45 

4 

0.06981  32 

64 

1.1170107 

124 

2.16420  83 

4 

0.0011636 

4 

0.00001  94 

5 

0.08726  65 

65 

1.1344640 

125 

2.18166  16 

5 

0.00145  44 

5 

0.00002  42 

6 

0.10471  98 

66 

1.15191  73 

126 

2.19911  49 

G 

0.00174  53 

6 

0.00002  91 

7 

0.1221730 

67 

1.16937  06 

127 

2.21656  82 

7 

0.00203  62 

7 

0.00003  39 

8 

0.13962  63 

68 

1.1868239 

128 

2.23402  14 

8 

0.00232  71 

8 

0.00003  88 

9 

0.15707  96 

69 

1.20427  72 

129 

2.25147  47 

9 

0.00261  80 

9 

0.00004  36 

10 

0.17453  29 

70 

1.22173  05 

130 

2.26892  80 

10 

0.00290  89 

10 

0.00004  85 

11 

0.19198  62 

71 

1.2391838 

131 

2.28638  13 

11 

0.00319  98 

11 

0.00005  33 

12 

0.20943  95 

72 

1.25663  71 

132 

2.30383  46 

12 

0.00349  07 

12 

0.00005  82 

13 

0.22689  28 

73 

1.27409  04 

133 

2.32128  79 

13 

0.00378  15 

13 

0.00006  30 

14 

0.24434  61 

74 

1.29154  36 

134 

2.33874  12 

14 

0.00407  24 

14 

0.00006  79 

15 

0.26179  94 

75 

1.30899  69 

135 

2.35619  45 

15 

0.00436  33 

15 

0.00007  27 

16 

0.27925  27 

76 

1.32645  02 

136 

2.37364  78 

10 

0.00465  42 

16 

0.00007  76 

17 

0.29670  60 

77 

1.3439035 

137 

2.39110  11 

11 

0.00494  51 

17 

0.00008  24 

18 

0.3141593 

78 

1.36135  68 

138 

2.40855  44 

IS 

O.UU523  6U 

18 

0.00008  73 

19 

0.33161  26 

79 

1.37881  01 

139 

2.42600  77 

19 

0.00552  69 

19 

0.00009  21 

20 

0.34906  59 

80 

1.39626  34 

140 

2.44346  10 

20 

0.00581  78 

20 

0.00009  70 

21 

0.36651  91 

81 

1.41371  67 

141 

2.46091  42 

21 

0.00610  87 

21 

0.00010  18 

22 

0.38397  24 

82 

1.43117  00 

142 

2.47836  75 

22 

0.00639  95 

22 

0.00010  67 

23 

0.40142  57 

83 

1.44862  33 

143 

2.49582  08 

23 

0.00669  04 

23 

0.00011  15 

24 

0.41887  90 

84 

1.46607  66 

144 

2.51327  41 

24 

0.00698  13 

24 

0.00011  64 

25 

0.43633  23 

(85^ 

1.48352  99 

145 

2.53072  74 

25 

0.00727  22 

25 

0.00012  12 

26 

0.45378  56 

86 

1.50098  32 

146 

2.54818  07 

26 

0.00756  31 

26 

0.00012  61 

27 

0.47123  89 

87 

1.51843  64 

147 

2.56563  40 

27 

0.00785  40 

27 

0.00013  09 

28 

0.48869  22 

88 

1.53588  97 

148 

2.58308  73 

28 

0.00814  49 

28 

0.00013  57 

29 

0.50614  55 

89 

1.55334  30 

149 

2.60054  06 

29 

0.00843  58 

29 

0.00014  06 

30 

0.52359  88 

90 

1.57079  63 

150 

2.61799  39 

30 

0.00872  66 

30 

0.00014  54 

31 

0.54105  21 

91 

1.5882496 

151 

2.63544  72 

31 

0.00901  75 

31 

0.00015  03 

32 

0.55850  54 

92 

1.60570  29 

152 

2.65290  05 

32 

0.00930  84 

32 

0.00015  51 

33 

0.57595  87 

93 

1.62315  62 

153 

2.67035  38 

33 

0.00959  93 

33 

0.00016  00 

34 

0.59341  19 

94 

1.6406095 

154 

2.68780  70 

34 

0.00989  02 

34 

0.00016  48 

35 

0.61086  52 

95 

1.65806  28 

155 

2.70526  03 

35 

0.01018  11 

35 

0.00016  97 

36 

0.62831  85 

96 

1.67551  61 

156 

2.72271  36 

36 

0.01047  20 

#6-, 

0.00017  45 

37 

0.64577  18 

97 

1.69296  94 

157 

2.74016  69 

37 

0.01076  29 

37 

0.00017  94 

38 

0.66322  51 

98 

1.71042  27 

158 

2.75762  02 

38 

0.0110538 

38 

0.00018  42 

39 

0.68067  84 

99 

1.72787  60 

159 

2.77507  35 

39 

0.0113446 

39 

0.00018  91 

40 

0.69813  17 

100 

1.7453293 

160 

2.79252  68 

40 

0.01163  55 

40 

0.00019  39 

41 

0.71558  50 

101 

1.76278  25 

161 

2.80998  01 

41 

0.01192  64 

41 

0.00019  88 

42 

0.73303  83 

102 

1.78023  58 

162 

2.82743  34 

42 

0.01221  73 

42 

0.00020  36 

43 

0.75049  16 

103 

1.79768  91 

163 

2.84488  67 

43 

0.01250  82 

43 

0.00020  85 

44 

0.76794  49 

104 

1.81514  24 

164 

2.86234  00 

44 

0.01279  91 

44 

0.00021  33 

45 

0.78539  82 

105 

1.83259  57 

165 

2.87979  33 

45 

0.01309  00 

45 

0.00021  82 

46 

0.80285  15 

106 

1.85004  90 

166 

2.89724  66 

46 

0.01338  09 

46 

0.00022  30 

47 

0.82030  47 

107 

1.8675023 

167 

2.91469  99 

47 

0.01367  17 

47 

0.00022  79 

48 

0.83775  80 

108 

1.88495  56 

168 

2.93215  31 

4S 

0.01396  26 

48 

0.00023  27 

49 

0.85521  13 

109 

1.90240  89 

169 

2.94960  64 

49 

0.01425  35 

49 

0.00023  76 

50 

0.87266  46 

110 

1.91986  22 

170 

2.96705  97 

50 

0.01454  44 

50 

0.00024  24 

51 

0.89011  79 

111 

1.93731  55 

171 

2.98451  30 

51 

0.01483  53 

51 

0.00024  73 

52 

0.90757  12 

112 

1.95476  88 

172 

3.00196  63 

52 

0.01512  62 

52 

0.00025  21 

53 

0.92502  45 

113 

1.97222  21 

173 

3.01941  96 

33 

0.01541  71 

53 

0.00025  70 

54 

0.94247  78 

114 

1.98967  53 

174 

3.03687  29 

54 

0.01570  80 

54 

0.00026  18 

55 

0.95993  11 

115 

2.00712  86 

175 

3.05432  62 

55 

0.01599  89 

55 

0.00026  66 

56 

0.97738  44 

116 

2.02458  19 

176 

3.07177  95 

36 

0.01628  97 

56 

0.00027  15 

57 

0.99483  77 

117 

2.04203  52 

177 

3.08923  28 

157 

0.01658  06 

57 

0.00027  63 

58 

1.01229  10 

118 

2.05948  85 

178 

3.1066861 

58 

0.01687  15 

58 

0.00028  12 

59 

1.0297443 

119 

2.07694  18 

179 

3.12413  94 

59 

0.0171624 

59 

0.00028  60 

60 

1.04719  76 

120 

2.09439  51 

180 

3.14159  27 

60 

0.01745  33 

60 

0.00029  09 

92    Table  V  —  Radian  Measure  —  Trigonometric  Functions    [V 


0) 

-3 

1 

« 

Sin  * 

Cos  x 

Tan* 

Equivalent 
of* 

CO 
• 

1 

H 

Sin* 

Cos  * 

Tan* 

Equivalent 
of* 

.00 

.00000 

1.0000 

.00000 

0°  OO'.O 

.50 

.47943 

.87758 

.54630 

28°  38'.9 

.01 
.02 
.03 

.01000 
.02000 
.03000 

.99995 
.99980 
.99955 

.01000 
.02000 
.03001 

0°  34'.4 
1°  08'.8 
1°  43'.1 

.51 
.52 
.53 

.48818 
.49688 
.50553 

.87274 
.86782 
.86,^81 

.55936 
.57256 
.58592 

29°  13'.3 
29°  47'.6 
30°  22'.0 

.04 
.05 
.06 

.03999 
.04998 
.05996 

.99920 
.99875 
.99820 

.04002 
.05004 
.06007 

2°  17'.5 
2°  51'.9 
3°  26'.3 

.54 
.55 
.56 

.51414 
.52269 
.53119 

.85771 
.85252 
.84726 

.59943 
.61311 
.62695 

30°  56'.4 
31°  30'.8 
32°  OS'.l 

.07 
.08 
.09 

.06994 
.07991 
.08988 

.99755 
.99680 
.99595 

.07011 
.08017 
.09024 

4°  00'.6 
4°  35'.0 
5°  09'.4 

.57 

.58 
.59 

.53963 
.54802 
.55636 

.84190 
.83646 
.83094 

.64097 
.65517 
.66956 

32°  39'.5 
33°  13'.9 
33°  48'.3 

.10 

.09983 

.99500 

.10033 

5°  43'.8 

.60 

.56464 

.82534 

.68414 

34°  22'.6 

.11 
.12 
.13 

.10978 
.11971 
.12963 

.99396 
.99281 
.99156 

.11045 
.12058 
.13074 

6°  18'.2 
6°  52'.5 
7°  26'.9 

.61 
.62 
.63 

.57287 
.58104 
.58914 

.81965 
.81388 
.80803 

.69892 
.71391 
.72911 

34°  57'.0 
35°  31'.4 
36°  05'.8 

.14 
.15 
.16 

.13954 
.14944 
.15932 

.99022 

.98877 
.98723 

.14092 
.15114 
.16138 

8°  01'.3 
8°  35'.7 
9°  lO'.O 

.64 
.65 
.66 

.59720 
.60519 
.61312 

.80210 
.79608 
.78999 

.74454 

.76020 
.77610 

36°  40'.2 
37°  14'.5 
37°  48'.9 

.17 
.18 
.19 

.16918 
.17903 

.18886 

.98558 
.98384 
.98200 

.17166 
.18197 
.19232 

9°  44'.4 
10°  18'.8 
10°  53'.2 

.67 

.68 
.69 

.62099 
.62879 
.63654 

.78382 
.77757 
.77125 

.79225 

.80866 
.82534 

38°  23'.3 
38°  57'.7 
39°  32'.0 

.20 

.19867 

.98007 

.20271 

11°27'.5 

.70 

.64422 

.76484 

.84229 

40°  06'.4 

.21 
.22 
.23 

.20846 
.21823 
.22798 

.97803 
.97590 
.97367 

.21314 
.22362 
.23414 

12°  01'.9 
12°  36'.3 
13°  10'.7 

.71 
.72 
.73 

.65183 
.65938 
.66687 

.75836 
.75181 
.74517 

.85953 
.87707 
.89492 

40°  40'.8 
41°  15'.2 
41°49'.6 

.24 

.25 
.26 

.23770 
.24740 
.25708 

.97134 
.96891 
.96639 

.24472 
.25534 
.26602 

13°45'.l 
14°  19'.4 
14°  53'.8 

.74 
.75 
.76 

.67429 
.68164 
.68892 

.73847 
.73169 

.72484 

.91309 
.93160 
.95045 

42°  23'.9 
42°  58'.3 
43°  32'.7 

.27 

.28 
.29 

.26673 
.27636 
.28595 

.96377 
.96106 
.95824 

.27676 
.28755 
.29841 

15°  28'.2 
16°  02'.6 
16°  36'.9 

.77 
.78 
.79 

.69614 
.70328 
.71035 

.71791 
.71091 
.70385 

.96967 
.98926 
1.0092 

44°  07'.  1 
44°  41  '.4 
45°  15'.8 

.30 

.29552 

.95534 

.30934 

17°  11'.  3 

.80 

.71736 

.69671 

1.0296 

45°  50'.2 

.31 
.32 
.33 

.30506 
.31457 
.32404 

.95233 
.94924 
.94604 

.32033 
.33139 
.34252 

17°  45'.7 
18°  20M 
18°  54'.5 

.81 
.82 
.83 

.72429 
.73115 
.73793 

.68950 
.68222 
.67488 

1.0505 
1.0717 
1.0934 

46°  24'.6 
46°  59'.0 
47°  33'.3 

.34 
.35 
.36 

.33349 
.34290 
.35227 

.94275 
.93937 
.93590 

.35374 
.36503 
.37640 

19°  28'.8 
20°  03'.2 
20°  37'.6 

.84 

.85 
.86 

.74464 
.75128 

.75784 

.66746 
.65998 
.65244 

1.1156 
1.1383 
1.1616 

48°  07'.7 
48°  42M 
49°  16'.5 

.37 

.38 
.39 

.36162 
.37092 
.38019 

.93233 

.92866 
.92491 

.38786 
.39941 
.41105 

21°  12'.0 
21°46'.3 

22°  20'.7 

.87 
.88 
.89 

.76433 

.77074 
.77707 

.64483 
.63715 
.62941 

1.1853 
1.2097 
1.2346 

49°  50'.8 
5C°  25'.2 
50°  59'.6 

.40 

.38942 

.92106 

.42279 

22°  55M 

.90 

.78333 

.62161 

1.2602 

51°  34'.0 

.41 
.42 
.43 

.39861 
.40776 
.41687 

.91712 
.91309 
.90897 

.43463 
.44657 
.45862 

23°  29'.5 
24°  03'.9 
24°  38'.2 

.91 
.92 
.93 

.78950 
.79560 
.80162 

.61375 
.60582 
.59783 

1.2864 
1.3133 
1.3409 

52°  08'.3 
52°  42'.7 
53°  17M 

.44 
.45 
.46 

.42594 
.43497 
.44395 

.90475 
.90045 
.89605 

.47078 
.48306 
.49545 

25°  12'.6 

25°  47'.0 
26°  21'.4 

.94 
.95 
.96 

.80756 
.81342 
.81919 

.58979 
.58168 
.57352 

1.3692 
1.3984 
1.4284 

53°  51'.5 
54°  25'.9 
55°  00'.2 

.47 
.48 
.49 

.45289 
.46178 
.47063 

.89157 
.88699 
.88233 

.50797 
.52061 
.53339 

26°  55'.7 
27°30'.l 
28°  04'.5 

.97 
.98 
.99 

.82489 
.83050 
.83603 

.56530 
.55702 
.54869 

1.4592 
1.4910 
1  .5237 

55°  34'.6 
56°  09'.0 
56°  43'.4 

.50 

.47943 

.87758 

.54630 

28°  :-S8'.9 

1.00 

.84147 

.54030 

1.5574 

57°  17'.7 

V] 


Radian  Measure  —  Tngonometric  Functions 


93 


x  Radians 

Sin* 

Cos* 

Tan* 

Equivalent 
of* 

*  Radians 

Sin* 

Cos  * 

Tan* 

Equivalent 
of* 

1.00 

.84147 

.54030 

1.5574 

57°  17'.7 

1.30 

.96356 

.26750 

3.6021 

74°  29'.  1 

1.01 
1.02 
1.03 

.84683 
.85211 
.85730 

.53186 
.52337 
.51482 

1.5922 
1.6281 
1.6652 

57°  52'.  1 
58°  26'.5 
59°  00'.9 

1.31 
1.32 
1.33 

.96618 
.96872 
.97115 

.25785 
.24818 
.23848 

3.7471 
3.9033 
4.0723 

75°  08'.4 
75°  37'.8 
76°  12'.2 

1.04 
1.05 
1.06 

.86240 
.86742 
.87236 

.50622 
.49757 

.48887 

1.7036 
1.7433 
1.7844 

59°  35'.3 
60°  09'.6 
60°  44'.0 

1.34 
1.35 
1.36 

.97348 
.97572 
.97786 

.22875 
.21901 
.20924 

4.2556 
4.4552 
4.6734 

76°  46'.6 
77°  21'.0 
77°  55'.3 

1.07 
1.08 
1.09 

.87720 
.88196 
.88663 

.48012 
.47133 
.46249 

1.8270 
1.8712 
1.9171 

61°  18'.4 
61°  52'.8 
62°  27M 

1.37 
1.38 
1.39 

.97991 
.98185 
.98370 

.19945 
.18964 
.17981 

4.9131 
5.1774 
5.4707 

78°  29'.7 
79°  O4'.l 
79°  38'.5 

1.10 

.89121 

.45360 

1.9648 

63°  Ol'.S 

1.40 

.98545 

.16997 

5.7979 

80°  12'.8 

1.11 

1.12 
1.13 

.89570 
.90010 
.90441 

.44466 
.43568 
.42666 

2.0143 
2.0660 
2.1198 

63°  35'.9 
64°  10'.3 
64°  44'.7 

1.41 
1.42 
1.43 

.98710 
.98865 
.99010 

.16010 
.15023 
.14033 

6.1654 
6.5811 
7.0555 

80°  47'.2 
81°  21'.  6 
81°  56'.0 

1.14 
1.15 
1.16 

.90863 
.91276 
.91680 

.41759 
.40849 
.39934 

2.1759 
2.2345 
2.2958 

65°  19'.0 
65°  53'.4 
66°  27'.8 

1.44 
1.45 
1.46 

.99146 
.99271 
.99387 

.13042 
.12050 
.11057 

7.6018 
8.2381 
8.9886 

82°  30'.4 
83°  04'.7 
83°  39'.1 

1.17 
1.18 
1.19 

.92075 
.92461 
.92837 

.39015 
.38092 
.37166 

2.3600 
2.4273 
2.4979 

67°  02'.2 
67°  36'.5 
68°  10f.9 

1.47 
1.48 
1.49 

.99492 
.99588 
.99674 

.10063 
.09067 
.08071 

9.8874 
10.983 
12.350 

84°  13'.5 
84°  47'.9 
85°  22'.2 

1.20 

.93204 

.36236 

2.5722 

68°  45'.3 

1.50 

.99749 

.07074 

14.101 

85°  56'.6 

1.21 
1.22 
1.23 

.93562 
.93910 
.94249 

.35302 
.34365 
.33424 

2.6503 
2.7328 
2.8198 

69°  19'.7 
69°  54'.  1 
70°  28'  A 

1.51 
1.52 
1.53 

.99815 
.99871 
.99917 

.06076 
.05077 
.04079 

16.428 
19.670 
24.498 

86°  31'.0 
87°  05'.4 
87°  39'.8 

1.24 
1.25 
1.26 

.94578 
.94898 
.95209 

.32480 
.31532 
.30582 

2.9119 
3.0096 
3.1133 

71°  02'.8 
71°  37'.2 
72°  11'.6 

1.54 
1.55 
1.56 

.99953 
.99978 
.99994 

.03079 
.02079 
.01080 

32.461 
48.078 
92.621 

88°  14'.  1 
88°  48'.5 
89°  22'.9 

1.27 
1.28 
1.29 

.95510 
.95802 
.96084 

.29628 
.28672 
.27712 

3.2236 
3.3413 
3.4672 

72°  45'.9 
73°  20'.3 
73°  54'.7 

•1.57 

•1.0000 

•.00080 

•1255.8 

89°  57'.3 

1.58 
1.59 

.99996 
.99982 

-.00920 
-.01920 

-108.65 
-52.067 

90°  31'.6 
91°  06'.0 

1.30 

.96356 

.26750 

3.6021 

74°29'.l 

1.60 

.99957 

-.02920 

-34.233 

91°40'.4 

IT  radians  =  180° 

•K  =  3.14159265 

*1  right  angle  =  90° 


1  radian  =  57°  17'  44".806  =  57.°2957795 
3600"  =  60'  =  1°  =  0.01745329  radian 
T/2  radians  =  1.5707963  radians 


Table  Va  —  Radians  to  Degrees 


RADIANS 

TBNTHS 

HUNDREDTHS 

THOUSANDTHS 

T*N-THOUSANDTHS 

1 

57°17'44".8 

5°43'46".5 

0°34'22".6 

0°  3'26".3 

0°  0'20".6 

2 

114°35'29".6 

11°27'33".0 

1°  8'45".3 

0°  6'52".5 

0°  0'41".3 

3 

171°53'14".4 

17°11'19".4 

1°43'07".9 

0°10'18".8 

0°  1'01".9 

4 

229°10'59".2 

22°55'05".9 

2°17'30".6 

0°13'45".l 

0°  1'22".5 

5 

286°28'44".0 

28°38'52".4 

2°51'53".2 

0°17'11".3 

0°  l'43".l 

6 

343°46'28".8 

34°22'38".9 

3°26'15".9 

0°20'37".6 

0°  2'03".8 

7 

401°  4'13".6 

40°  6'25".4 

4°  0'38".5 

0°24'03".9 

0°  2'24".4 

8 

458°21'58".4 

45°50'11".8 

4°35'01".2 

0°27'30".l 

0°  2'45".0 

9 

515°39'43".3 

51°33'58".3 

5°  9'23'  .8 

0°30'56".4 

0°  3'05".6 

94 


Table  VI  —  Powers  —  Roots  —  Reciprocals 


[VI 


n 

n2 

V7T 

VlOn 

7l3 

^ 

^10  n 

^100  n 

l/n 

1.00 

1.0000 

1.00000 

3.16228 

1.00000 

1.00000 

2.15443 

4.64J59 

1.00000 

1.01 
1.02 
1.03 

1.0201 
1.0404 
1.0609 

1.00499 
1.00995 
1.01489 

3.  J  7805 
3.19374 
3.20936 

1.03030 
1.06121 
1.09273 

1.00332 
1.00662 
1.00990 

2.16159 
2.16870 
2.17577 

4.65701 
4.67233 
4.68755 

.990099 
.980392 
.970874 

1.04 
1.05 
1.06 

1.0816 
1.1025 
1.1236 

1.01980 
1.02470 
1.02956 

3.22490 
3.24037 
3.25576 

1.12486 
1.15762 
1.19102 

1.01316 
1.01640 
1.01961 

2.18279 
2.18976 
2.19669 

4.70267 
4.71769 
4.73262 

.961538 
.952381 
.943396 

1.07 
1.08 
1.09 

1.1449 
1.1664 
1.1881 

1.03441 
1.03923 
1.04403 

3.27109 
3.28634 
3.30151 

1.22504 
1.25971 
1.29503 

1.02281 
1.02599 
1.02914 

2.20358 
2.21042 
2.21722 

4.74746 
4.76220 
4.77686 

.934579 
.925926 
.917431 

1.10 

1.2100 

1.04881 

3.31662 

1.33100 

1.03228 

2.22398 

4.79142 

.909091 

1.11 
1.12 
1.13 

1.2321 
1.2544 
1.2769 

1.05357 
1.05830 
1.06301 

3.33167 
3.34664 
3.36155 

1.36763 
1.40493 
1.44290 

1.03540 
1.03850 
1.04158 

2.23070 
2.23738 
2.24402 

4.80590 
4.82028 
4.83459 

.900901 
.892857 
.884956 

1.14 
1.15 
1.16 

1.2996 
1.3225 
1.3456 

1.06771 
1.07238 
1.07703  . 

3.37639 
3.39116 
3.40588 

1.48154 
1.52088 
1.56090 

1.04464 
1.04769 
1.05072 

2.25062 
2.25718 
2.26370 

4.84881 
4.86294 
4.87700 

.877193 
.869565 
.862069 

1.17 

1.18 
1.19 

1.3689 
1.3924 
1.4161 

1.08167 
1.08628 
1.09087 

3.42053 
3.43511 

3.44964 

1.60161 
1.64303 
1.68516 

1.05373 
1.05672 
1.05970 

2.27019 
2.27664 
2.28305 

4.89097 
4.90487 
4.91868 

.854701 

.847458 
.840336 

1.20 

1.4400 

1.09545 

3.46410 

1.72800 

1.06266 

2.28943 

4.93242 

.833333 

1.21 
1.22 
1.23 

1.4641 
1.4884 
1.5129 

1.10000 
1.10454 
1.10905 

3.47851 
3.49285 
3.50714 

1.77156 
1.81585 
1.86087 

1.06560 
1.06853 
1.07144 

2.29577 
2.30208 
2.30835 

4.94609 
4.95968 
4.97319 

.826446 
.819672 
.813008 

1.24 
1.25 
1.26 

1.5376 
1.5625 
1.5876 

1.11355 
1.118031' 
1.12250 

3.52136 
3.53553 
3.54965 

1.90662 
1.95312 
2.00038 

1.07434 
1.07722 
1.08008 

2.31459 
2.32079 
2.32697 

4.98663 
5.00000 
5.01330 

.806452 
.800000 
.793651 

1.27 
1.28 
1.29 

1.6129 
1.6384 
1.6641 

1.12694 
1.13137 
1.13578 

3.56371 
3.57771 
3.59166 

2.04838 
2.09715 
2.14669 

1.08293 

1.08577 
1.08859 

2.33311 
2.33921 
2.34529 

5.02653 
5.03968 
5.05277 

.787402 
.781250 
.775194 

1.30 

1.6900 

1.14018 

3.60555 

2.19700 

1.09139 

2.35133 

5.06580 

.769231 

1.31 
1.32 
1.33 

1.7161 
1.7424 
1.7689 

1.14455 
1.14891 
1.15326 

3.61939 
3.63318 
3.64692 

2.24809 
2.29997 
2.35264 

1.09418 
1.09696 
1.09972 

2.35735 
2.36333 

2.36928 

5.07875 
5.09164 
5.10447 

.763359 
.757576 
.751880 

1.34 
1.35 
1.36 

1.7956 
1.8225 
1.8496 

1.15758 
1.16190 
1.16619 

3.66060 

3.67423 
3.68782 

2.40610 
2.46038 
2.51546 

1.10247 
1.10521 
1.10793 

2.37521 
2.38110 
2.38697 

5.11723 
5.12993 
5.14256 

.746269 
.740741 
.735294 

1.37 

1.38 
1.39 

1.8769 
1.9044 
1.9321 

1.17047 
1.17473 

1.17898 

3.70135 

3.71484 
3.72827 

2.57135 

2.62807 
2.68562 

1.11064 
1.11334 
1.11602 

2.39280 
2.39861 
2.40439 

5.15514 
5.16765 
5.18010 

.729927 
.724638 
.719424 

1.40 

1.9600 

1.18322 

3.74166 

2.74400 

1.11869 

2.41014 

5.19249 

.714286 

1.41 
1.42 
1.43 

1.9881 
2.0164 
2.0449 

1.18743 
1.19164 
1.19583 

3.75500 
3.76829 
3.78153 

2.80322 
2.86329 
2.92421 

1.12135 
1.12399 
1.12662 

2.41587 
2.42156 
2.42724 

5.20483 
5.21710 
5.22932 

.709220 
.704225 
.699301 

1.44 
1.45 
1.46 

2.0736 
2.1025 
2.1316 

1.20000 
1.20416 
1.20830 

3.79473 
3.80789 
3.82099 

2.98598 
3.04862 
3.11214 

1.12924 
1.13185 
1.13445 

2.43288 
2.43850 
2.44409 

5.24148 
5.25359 
5.26564 

.694444 
.689655 
.684932 

1.47 
1.48 
1.49 

2.1609 
2.1904 
2.2201 

1.21244 
1.21655 
1.22066 

3.83406 
3.84708 
3.86005 

3.17652 
3.24179 
3.30795 

1.13703 
1.13960 
1.14216 

2.44966 
2.45520 
2.46072 

5.27763 
5.28957 
5.30146 

.680272 
.675676 
.671141 

1.50 

2.2500 

1.22474 

3.87298 

3.37500 

1.14471 

2.46621 

5.31329 

.666667 

n 

n2 

V^ 

^[Wn 

n3 

3/  — 

Vn 

JIW71 

^100  n 

l/n 

VI] 


Powers  —  Roots  —  Reciprocals 


n 

n2 

V>7 

VlOn 

Fi3 

31  

\re 

\  10  Fl 

\100Fl 

1/Fl 

1.50 

2.2500 

1.22474 

3.87298 

3.37500 

1.14471 

2.46621 

5.31329 

.606667 

1.51 
1.52 
1.53 

2.2801 
2.3104 
2.3409 

1.22882 
1.23288 
1.23693 

3.88587 
3.89872 
3.91152 

3.44295 
3.51181 
3.58158 

1.14725 
1.14978 
1.15230 

2.47168 
2.47712 
2.48255 

5.32507 
5.33680 
5.34848 

.662252 
.657895 
.653595 

1.54 
1.55 
1.56 

2.3716 
2.4025 
2.4336 

1.24097 
1.24499 
1.24900 

3.92428 
3.93700 
3.94968 

3.65226 
3.72388 
3.79642 

1.15480 
1.15729 
1.15978 

2.48794 
2.49332 
2.49867 

5.36011 
5.37169 
5.38321 

.649351 
.645161 
.641026 

1.57 
1.58 
1.59 

2.4649 
2.4964 

2.5281 

1.25300 
1.25698 
1.26095 

3.96232 
3.97492 
3.98748 

3.86989 
3.94431 
4.01968 

1.16225 
1.16471 
1.16717 

2.50399 
2.50930 
2.51458 

5.39469 
5.40612 
5.41750 

.636943 
.632911 
.628931 

1.60 

2.5600 

1.26491 

4.00000 

4.09600 

1.16961 

2.51984 

5.42884 

.625000 

1.61 
1.62 
1.63 

2.5921 
2.6244 
2.6569 

1.26886 
1.27279 
1-27671 

4.01248 
4.02492 
4.03733 

4.17328 
4.25153 
4.33075 

1.17204 
1.17446 
1.17687 

2.52508 
2.53030 
2.53549 

5.44012 
5.45136 
5.46256 

.621118 
.617284 
.613497 

1.64 
1.65 
1.66 

1.67 
1.68 
1.69 

2.3896 
2.7225 
2.7556 

2^889 
2.8224 
2.8561 

1.28062 
1.28452 
1.28841 

1.29228 
1.29615 
1.30000 

4.04969 
4.06202 
4.07431 

4.08656 
4.09878 
4.11096 

4.41094 
4.49212 
4.57430 

4.65746 
4.74163 

4.82681 

1.17927 
1.18167 
1.18406 

1.18642 
1.18878 
1.19114 

2.54067 
2.54582 
2.55095 

2.55607 
2.56116 
2.56623 

5.47370 
5.48481 
5.49586 

5.50688 
5.51785 
5.52877 

.609756 
.606061 
.602410 

.598802 
.595238 
.591716 

1.70 

2.8900 

1.30384 

4.12311 

4.91300 

1.19348 

2.57128 

5.53966 

.588235 

1.71 
1.72 
1.73 

2.9241 
2.9584 
2.9929 

1.30767 
1.31149 
1.31529 

4.13521 
4.14729 
4.15933 

5.00021 
5.08845 
5.17772 

1.19582 
1.19815 
1.20046 

2.57631 
2.58133 
2.58632 

5.55050 
5.56130 
5.57205 

.584795 
581395 
.578035 

1.74 
1.75 
1.76 

3.0276 
3.0625 
3.0976 

1.31909 
1.32288 
1.32665 

4.17133 
4.18330 
4.19524 

5.26802 
5.35938 
5.45178 

1.20277 
1.20507 
1.20736 

2.59129 
2.59625 
2.60118 

5.58277 
5.59344 
5.60408 

.574713 
.571429 
.568182 

1.77 

1.78 
1.79 

3.1329 
3.1684 
3.2041 

1.33041 
1.33417 
1.33791 

4.20714 
4.21900 
4.23084 

5.54523 
5.63975 
5.73534 

1.20964 
1.21192 
1.21418 

2.60610 
2.61100 
2.61588 

5.61467 
5.62523 
5.63574 

.564972 
.561798 
.558659 

1.80 

3.2400 

1.34164 

4.24264 

5.83200 

1.21644 

2.62074 

5.64622 

.555556 

1.81 
1.82 
1.83 

3.2761 
3.3124 
3.3489 

1.34536 
1.34907 
1.35277 

4.25441 
4.26615 
4.27785 

5.92974 
6.02857 
6.12849 

1.21869 
1.22093 
1.22316 

2.62559 
2.63041 
2.63522 

5.65665 
5.66705 
5.67741 

.552486 
.549451 
.546448 

1.84 
1.85 
1.86 

3.3856 
3.4225 
3.4596 

1.35647 
1.36015 
1.36382 

4.28952 
4.30116 
4.31277 

6.22950 
6.33162 
6.43486 

1.22539 
1.22760 
1.22981 

2.64001 
2.64479 
2.64954 

5.68773 
5.69802 
5.70827 

.543478 
.540541 
.537634 

1.87 
1.88 
1.89 

3.4969 
3.5344 
3.5721 

1.36748 
1.37113 
1.37477 

4.32435 
4.33590 
4.34741 

6.53920 
6.64467 
6.75127 

1.23201 
1.23420 
1.23639 

2.65428 
2.65901 
2.66371 

5.71848 
5.72865 
5.73879 

.534759 
.531915 
.529101 

1.90 

3.6100 

1.37840 

4.35890 

6.85900 

1.23856 

2.66840 

5.74890 

.526316 

1.91 
1.92 
1.93 

3.6481 
3.6864 
3.7249 

1.38203 
1.38564 
1.38924 

4.37035 
4.38178 
4.39318 

6.96787 
7.07789 
7.18906 

1.24073 
1.24289 
1.24505 

2.67307 
2.67773 
2.68237 

5.75897 
5.76900 
5.77900 

.523560 
.520833 
.518135 

1.94 
1.95 
1.96 

3.7636 
3.8025 
3.8416 

1.39284 
1.39642 
1.40000 

4.40454 
4.41588 
4.42719 

7.30138 
7.41488 
7.52954 

1.24719 
1.24933 
1.25146 

2.68700 
2.69161 
2.69620 

5.78896 
5.79889 
5.80879 

.515464 
.512821 
.510204 

1.97 
1.98 
1.99 

3.8809 
3.9204 
3.9601 

1.40357 
1.40712 
1.41067 

4.43847 
4.44972 
4.46094 

7.64537 
7.76239 

7.88060 

1.25359 
1.25571 
1.25782 

2.70078 
2.70534 
2.70989 

5.81865 
5.82848 
5.83827 

.507614 
.505051 
.502513 

2.00 

4.0000 

1.41421 

4.47214 

8.00000 

1.25992 

2.71442 

5.84804 

.500000 

n. 

n2 

vs 

VlO  n 

Fi3 

3/  — 

\n 

^10  n 

x'lOOn 

1/Fl 

• 


96 


Powers  —  Roots  —  Reciprocals 


[VI 


n 

n2 

V^ 

VToTI 

n3 

•\ln 

^10  n 

A'100  11 

l/n 

2.00 

4.0000 

1.41421 

4.47214 

8.00000 

1.25992 

2.71442 

5.84804 

.500000 

2.01 
2.02 
2.03 

4.0401 
4.0804 
4.1209 

1.41774 
1.42127 
1.42478 

4.48330 
4.49444 
4.50555 

8.12060 
8.24241 
8.36543 

1.26202 
1.26411 
1.26619 

2.71893 
2.72344 
2.72792 

5.85777 
5.86746 
5.87713 

.497512 
.495050 
.492611 

2.04 
2.05 
2.06 

4.1616 
4.2025 
4.2436 

1.42829 
1.43178 
1.43527 

4.51664 
4.52769 
4.53872 

8.48966 
8.61512 
8.74182 

1.26827 
1.27033 
1.27240 

2.73239 
2.73685 
2.74129 

5.88677 
5.89637 
5.90594 

.490196 
.487805 
.485437 

2.07 
2.08 
2.09 

4.2849 
4.3264 
4.3681 

1.43875 
1.44222 
1.44568 

4.54973 
4.56070 
4.57165 

8.86974 
8.99891 
9.12933 

1.27445 
1.27650 
1.27854 

2.74572 
2.75014 
2.75454 

5.91548 
5.92499 
5.93447 

.483092 
.480769 
.478469 

2.10 

4.4100 

1.44914 

4.58258 

9.26100 

1.28058 

2.75892 

5.94392 

.476190 

2.11 
2.12 
2.13 

4.4521 
4.4944 
4.5369 

1.45258 
1.45602 
1.45945 

4.59347 
4.60435 
4.61519 

9.39393 
9.52813 
9.66360 

1.28261 
1.28463 
1.28665 

2.76330 
2.76766 
2.77200 

5.95334 
5.96273 
5.97209 

.473934 
.471698 
.469434 

2.14 
2.15 
2.16 

4.5796 
4.6225 
4.6656 

1.46287 
1.46629 
1.46969 

4.62601 
4.63681 
4.64758 

9.80034 
9.93838 
10.0777 

1.28866 
1.29066 
1.29266 

2.77633 
2.78065 
2.78495 

5.98142 
5.99073 
6.00000 

.467290 
.465116 
.462963 

2.17 
2.18 
2.19 

4.7089 
4.7524 
4.7961 

1.47309 
1.47648 
1.47986 

4.65833 
4.66905 
4.67974 

10.2183 
10.3602 
10.5035 

1.29465 
1.29664 
1.29862 

2.78924 
2.79352 
2.79779 

6.00925 
6.01846 
6.02765 

.460829 
.458716 
.456621 

2.20 

4.8400 

1.48324 

4.69042 

10.6480 

1.30059 

2.80204 

6.03681 

.454545 

2.21 
2.22 
2.23 

4.8841 
4.9284 
4.9729 

1.48661 
1.48997 
1.49332 

4.70106 
4.71169 
4.72229 

10.7939 
10.9410 
11.0896 

1.30256 
1.30452 
1.30648 

2.80628 
2.81050 
2.81472 

6.04594 
6.05505 
6.06413 

.452489 
.450450 
.448430 

2.24 
2.25 
2.26 

5.0176 
5.0625 
5.1076 

1.49666 
1.50000 
1.50333 

4.73286 
4.74342 
4.75395 

11.2394 
11.3906 
11.5432 

1.30843 
1.31037 
1.31231 

2.81892 
2.82311 

2.82728 

6.07318 
6.08220 
6.09120 

.446429 
.444444 

.442478 

2.27 
2.28 
2.29 

5.1529 
5.1984 
5.2441 

1.50665 
1.50997 
1.51327 

4.76445 
4.77493 
4.78539 

11.6971 
11.8524 
12.0090 

1.31424 
1.31617 
1.31809 

2.83145 
2.83560 
2.83974 

6.10017 
6.10911 
6.11803 

.440529 
.438596 
.436681 

2.30 

5.2900 

1.51658 

4.79583 

12.1670 

1.32001 

2.84387 

6.12693 

.434783 

2.31 
2.32 
2.33 

5.3361 
5.3824 
5.4289 

1.51987 
1.52315 
1.52643 

4.80625 
4.81664 
4.82701 

12.3264 
12.4872 
12.6493 

1.32192 
1.32382 
1.32572 

2.84798 
2.85209 
2.85618 

6.13579 
6.14463 
6.15345 

.432900 
.431034 

.429185 

2.34 
2.35 
2.36 

5.4756 
5.5225 
5.5696 

1.52971 
1.53297 
1.53623 

4.83735 
4.84768 
4.85798 

12.8129 
12.9779 
13.1443 

1.32761 
1.32950 
1.33139 

2.86026 
2.86433 
2.86838 

6.16224 
6.17101 
6.17975 

.427350 
.425532 
.423729 

2.37 
2.38 
2.39 

5.6169 
5.6644 
5.7121 

1.53948 
1.54272 
1.54596 

4.86826 
4.87852 
4.88876 

13.3121 
13.4813 
13.6519 

1.33326 
1.33514 
1.33700 

2.87243 
2.87646 
2.88049 

6.18846 
6.19715 
6.20582 

.421941 
.420168 
.418410 

2.40 

5.7600 

1.54919 

4.89898 

13.8240 

1.33887 

2.88450 

6.21447 

.416667 

2.41 
2.42 
2.43 

5.8081 
5.8564 
5.9049 

1.55242 
1.55563 
1.55885 

4.90918 
4.91935 
4.92950 

13.9975 
14.1725 
14.3489 

1.34072 
1.34257 
1.34442 

2.88850 
2.89249 
2.89647 

6.22308 
6.23168 
6.24025 

.414938 
.413223 
.411523 

2.44 
2.45 
2.46 

5.9536 
6.0025 
6.0516 

1.56205 
1.56525 
1.56844 

4.93964 
4.94975 
4.95984 

14.5268 
14.7061 
14.8869 

1.34626 
1.34810 
1.34993 

2.90044 
2.90439 
2.90834 

6.24880 
6.25732 
6.26583 

.409836 
.408163 
.406504 

2.47 
2.48 
2.49 

6.1009 
6.1504 
6.2001 

1.57162 
1.57480 
1.57797 

4.96991 
4.97996 
4.98999 

15.0692 
15.2530 
15.4382 

1.35176 
1.35358 
1.35540 

2.91227 
2.91620 
2.92011 

6.27431 
6.28276 
6.29119 

.404858 
.403226 
.401606 

2.50 

6.2500 

1.58114 

5.00000 

15.6250 

1.35721 

2.92402 

6.29961 

.400000 

n 

n2 

V^ 

VlOn 

n3 

fti 

A/10  n 

^100  n 

l/n 

VI] 


Powers  —  Roots  —  Reciprocals 


97 


n 

n2 

V^ 

VlOn 

n3 

^ 

\10  71 

\100n 

l/n 

2.50 

6.2500 

1.58114 

5.00000 

15.6250 

1.35721 

2.92402 

6.29961 

.400000 

2.51 
2.52 
2.53 

6.3001 
6.3504 
6.4009 

1.58430 
1.58745 
1.59060 

5.00999 
5.01996 
5.02991 

15.8133 
16.0030 
16.1943 

1.35902 
1.36082 
1.36262 

2.92791 
2.93179 
2.93567 

6.30799 
6.31636 
6.32470 

.398406 
.396825 
.395257 

2.54 
2.55 
2.56 

6.4516 
6.5025 
6.5536 

1.59374 
1.59687 
1.60000 

5.03984 
5.04975 
5.05964 

16.3871 
16.5814 
16.7772 

1.36441 
1.36620 
1.36798 

2.93953 
2.94338 
2.94723 

6.33303 
6.34133 
6.34960 

.393701 
.392157 
.390625 

2.57 
2.58 
2.59 

6.6049 
6.6564 
6.7081 

1.60312 
1.60624 
1.60935 

5.06952 
5.07937 
5.08920 

16.9746 
17.1735 
17.3740 

1.36976 
1.37153 
1.37330 

2.95106 
2.95488 
2.95869 

6.35786 
6.36610 
6.37431 

.389105 
.387597 
.386100 

2.60 

6.7600 

1.61245 

5.09902 

17.5760 

1.37507 

2.96250 

6.38250 

.384615 

2.61 
2.62 
2.63 

6.8121 
6.8644 
6.9169 

1.61555 
1.61864 
1.62173 

5.10882 
5.11859 
5.12835 

17.7796 
17.9847 
18.1914 

1.37683 
1.37859 
1.38034 

2.96629 
2.97007 
2.97385 

6.39068 
6.39883 
6.40696 

.383142 
.381679 
.380228 

2.64 
2.65 
2.66 

6.9696 
7.0225 
7.0756 

1.62481 
1.62788 
1.63095 

5.13809 
5.14782 
5.15752 

18.3997 
18.6096 
18.8211 

1.38208 
1.38383 
1.38557 

2.97761 
2.98137 
2.98511 

6.41507 
6.42316 
6.43123 

.378788 
.377358 
.375940 

2.67 
2.68 
2.69 

7.1289 
7.1824 
7.2361 

1.63401 
1.63707 
1.64012 

5.16720 
5.17687 
5.18652 

19.0342 
19.2488 
19.4651 

1.38730 
1.38903 
1.39076 

2.98885 
2.99257 
2.99629 

6.43928 
6.44731 
6.45531 

.374532 
.373134 
.371747 

2.70 

7.2900 

1.64317 

5.19615 

19.6830 

1.39248 

3.00000 

6.46330 

.370370 

2.71 
2.72 
2.73 

7.3441 
7.3984 
7.4529 

1.64621 
1.64924 
1.65227 

5.20577 
5.21536 
5.22494 

19.9025 
20.1236 
20.3464 

1.39419 
1.39591 
1.39761 

3.00370 
3.00739 
3.01107 

6.47127 
6.47922 
6.48715 

.369004 
.367647 
.366300 

2.74 
2.75 
2.76 

7.5076 
7.5625 
7.6176 

1.65529 
1.65831 
1.66132 

5.23450 
5.24404 
5.25357 

20.5708 
20.7969 
21.0246 

1.39932 
1.40102 
1.40272 

3.01474 
3.01841 
3.02206 

6.49507 
6.50296 
6.51083 

.364964 
.363636 
.362319 

2.77 
2.78 
2.79 

7.6729 

7.7284 
7.7841 

1.66433 
1.66733 
1.67033 

5.26308 
5.27257 
5.28205 

21.2539 
21.4850 
21.7176 

1.40441 
1.40610 
1.40778 

3.02570 
3.02934 
3.03297 

6.51868 
6.52652 
6.53434 

.361011 
.359712 
.358423 

2.80 

7.8400 

1.67332 

5.29150 

21.9520 

1.40946 

3.03659 

6.54213 

.357143 

2.81 
2.82 
2.83 

7.8961 
7.9524 
8.0089 

1.67631 
1.67929 
1.68226 

5.30094 
6.31037 
5.31977 

22.1880 
22.4258 
22.6652 

1.41114 
1.41281 
1.41448 

3.04020 
3.04380 
3.04740 

6.54991 
6.55767 
6.56541 

.355872 
.354610 
.353357 

2.84 
2.85 
2.86 

8.0656 
8.1225 
8.1796 

1.68523 
1.68819 
1.69115 

5.32917 
5.33854 
5.34790 

22.9063 
23.1491 
23.3937 

1.41614 
1.41780 
1.41946 

3.05098 
3.05456 
3.05813 

6.57314 
6.58084 
6.58853 

.352113 

.350877 
.349650 

2.87 
2.88 
2.89 

8.2369 
8.2944 
8.3521 

1.69411 
1.69706 
1.70000 

5.35724 
5.36656 
5.37587 

23.6399 
23.8879 
24.1376 

1.42111 
1.42276 
1.42440 

3.06169 
3.06524 
3.06878 

6.59620 
6.60385 
6.61149 

.348432 
.347222 
.346021 

2.90 

8.4100 

1.70294 

5.38516 

24.3890 

1.42604 

3.07232 

6.61911 

.344828 

2.91 
2.92 
2.93 

8.4681 
8.5264 
8.5849 

1.70587 
1.70880 
1.71172 

5.39444 
5.40370 
5.41295 

24.6422 
24.8971 
25.1538 

1.42768 
1.42931 
1.43094 

3.07584 
3.07936 
3.08287 

6.62671 
6.63429 
6.64185 

.343643 
.342466 
.341297 

2.94 
2.95 
2.96 

8.6436 
8.7025 
8.7616 

1.71464 
1.71756 
1.72047 

5.42218 
5.43139 
5.44059 

25.4122 
25.6724 
25.9343 

1.43257 
1.43419 
1.43581 

3.08638 
3.08987 
3.09336 

6.64940 
6.65693 
6.66444 

.340136 
.338983 
.337838 

2.97 

2.98 
2.99 

8.8209 
8.8804 
8.9401 

1.72337 
1.72627 
1.72916 

5.44977 
5.45894 
5.46809 

26.1981 
26.4636 
26.7309 

1.43743 
1.43904 
1.44065 

3.09684 
3.10031 
3.10378 

6.67194 
6.67942 
6.68688 

.336700 
.335570 
.334448 

3.00 

9.0000 

1.73205 

5.47723 

27.0000 

1.44225 

3.10723 

6.69433 

.333333 

n 

n2 

V^ 

Vio  » 

n3 

3/  — 

Vn 

W^ 

^lOOT^ 

l/n 

98 


Powers  —  Roots  —  Reciprocals 


[VI 


11 

n? 

V^ 

VlOn 

n3 

In 

A/lOn 

^100  n 

1/n 

3.00 

9.0000 

1.73205 

5.47723 

27.0000 

1.44225 

3.10723 

6.69433 

.333333 

3.01 
3.02 
3.03 

9.0601 
9.1204 
9.1809 

1.73494 
1.73781 
1.74069 

5.48635 
5.49545 
5.50454 

27.2709 
27.5436 
27.8181 

1.44385 
1.44545 
1.44704 

3.11068 
3.11412 
3.11756 

6.70176 
6.70917 
6.71657 

.332226 
.331126 
.330033 

3.04 
3.05 
3.06 

9.2416 
9.3025 
9.3636 

1.74356 
1.74642 
1.74929 

5.51362 
5.52268 
5.53173 

28.0945 
28.3726 
28.6526 

1.44863 
1.45022 
1.45180 

3.12098 
3.12440 
3.12781 

6.72395 
6.73132 
6.73866 

.328947 
.327869 
.326797 

3.07 
3.08 
3.09 

9.4249 
9.4864 
9.5481 

1.75214 
1.75499 
1.75784 

5.54076 
5.54977 
5.55878 

28.9344 
29.2181 
29.5036 

1.45338 
1.45496 
1.45653 

3.13121 
3.13461 
3.13800 

6.74600 
6.75331 
6.76061 

.325733 
.324675 
.323625 

3.10 

9.6100 

1.76068 

5.56776 

29.7910 

1.45810 

3.14138 

6.76790 

.322581 

3.11 
3.12 
3.13 

9.6721 
9.7344 
9.7969 

1.76352 
1.76635 
1.76918 

5.57674 
5.58570 
5.59464 

30.0802 
30.3713 
30.6643 

1.45967 
1.46123 
1.46279 

3.14475 
3.14812 
3.15148 

6.77517 
6.78242 
6.78966 

.321543 
.320513 
.319489 

3.14 
3.15 
3.16 

9.8596 
9.9225 
9.9856 

1.77200 
1.77482 
1.77764 

5.60357 
5.61249 
5.62139 

30.9591 
31.2559 
31.6545 

1.46434 
1.46590 
1.46745 

3.15483 
3.15818 
3.16152 

6.79688 
6.80409 
6.81128 

.318471 
.317460 
.316456 

3.17 
3.18 
3.19 

10.0489 
10.1124 
10.1761 

1.78045 
1.78326 
1.78606 

5.63028 
5.63915 
5.64801 

31.8550 
32.1574 
32.4618 

1.46899 
1.47054 
1.47208 

3.16485 
3.16817 
3.17149 

6.81846 
6.82562 
6.83277 

.315457 
.314465 
.313480 

3.20 

10.2400 

1.78885 

5.65685 

32.7680 

1.47361 

3.17480 

6.83990 

.312500 

3.21 
3.22 
3.23 

10.3041 
10.3684 
10.4329 

1.79165 
1.79444 
1.79722 

5.66569 
5.67450 
5.68331 

33.0762 
33.3862 
33.6983 

1.47515 
1.47668 
1.47820 

3.17811 
3.18140 
3.18469 

6.84702 
6.85412 
6.86121 

.311526 
.310559 
.309598 

3.24 
3.25 
3.26 

10.4976 
10.5625 
10.6276 

1.80000 
1.80278 
1.80555 

5.69210 
5.70088 
5.70964 

34.0122 
34.3281 
34.6460 

1.47973 
1.48125 
1.48277 

3.18798 
3.19125 
3.19452 

6.86829 
6.87534 
6.88239 

.308642 
.307692 
.306748 

3.27 
3.28 
3.29 

10.6929 
10.7584 
10.8241 

1.80831 
1.81108 
1.81384 

5.71839 
5.72713 
5.73585 

34.9658 
35.2876 
35.6113 

1.48428 
1.48579 
1.48730 

3.19778 
3.20104 
3.20429 

6.88942 
6.89643 
6.90344 

.305810 
.304878 
.303951 

3.30 

10.8900 

1.81659 

5.74456 

35.9370 

1.48881 

3.20753 

6.91042 

.303030 

3.31 
3.32 
3.33 

10.9561 
11.0224 
11.0889 

1.81934 
1.82209 
1.82483 

5.75326 
5.76194 
5.77062 

36.2647 
36.5944 
36.9260 

1.49031 
1.49181 
1.49330 

3.21077 
3.21400 
3.21722 

6.91740 
6.92436 
6.93130 

.302115 
.301205 
.300300 

3.34 
3.35 
3.36 

11.1556 
11.2225 
11.2896 

1.82757 
1.83030 
1.83303 

5.77927 
5.78792 
5.79655 

37.2597 
37.5954 
37.9331 

1.49480 
1.49629 
1.49777 

3.22044 
3.22365 
3.22686 

6.93823 
6.94515 
6.95205 

.299401 
.298507 
.297619 

3.37 
3.38 
3.39 

11.3569 
11.4244 
11.4921 

1.83576 
1.83848 
1.84120 

5.80517 
5.81378 
5.82237 

38.2728 
38.6145 
38.9582 

1.49926 
1.50074 
1.50222 

3.23006 
3.23325 
3.23643 

6.95894 
6.96582 
6.97268 

.296736 

.295858 
.294985 

3.40 

11.5600 

1.84391 

5.83095 

39.3040 

1.50369 

3.23961 

6.97953 

.294118 

3.41 
3.42 
3.43 

11.6281 
11.6964 
11.7649 

1.84662 
1.84932 
1.85203 

5.83952 
5.84808 
5.85662 

39.6518 
40.0017 
40.3536 

1.50517 
1.50664 
1.50810 

3.24278 
3.24595 
3.24911 

6.98637 
6.99319 
7.00000 

.293255 
.292398 
.291545 

3.44 
3.45 
3.46 

11.8336 
11.9025 
11.9716 

1.85472 
1.85742 
1.86011 

5.86515 
5.87367 
5.88218 

40.7076 
41.0636 
41.4217 

1.50957 
1.51103 
1.51249 

3.25227 
3.25542 
3.25856 

7.00680 
7.01358 
7.02035 

.290698 
.289855 
.289017 

3.47 
3.48 
3.49 

12.0409 
12.1104 
12.1801 

1.86279 
1.86548 
1.86815 

5.89067 
5.89915 
5.90762 

41.7819 

42.1442 
42.5085 

1.51394 
1.51540 
1.51685 

3.26169 
3.26482 
3.26795 

7.02711 
7.03385 
7.04058 

.288184 
.287356 
.286533 

3.50 

12.2500 

1.87083 

5.91608 

42.8750 

1.51829 

3.27107 

7.04730 

.285714 

n 

n2 

V^ 

A/IoTi 

fl3 

31  — 

Vn 

sfto~^ 

^lOOn 

1/n 

VI] 


Powers  —  Roots  —  Reciprocals 


99 


n 

n2 

v^: 

VIoTi 

n3 

31  — 

Vn 

^10  n 

^100  n 

1/M 

3.50 

12.2500 

1.87083 

5.91608 

42.8750 

1.51829 

3.27107 

7.04730 

.285714 

3.51 
3.52 
3.53 

12.3201 
12.3904 
12.4609 

1.87350 

1.87617 
1.87883 

5.92453 
5.93296 
5.94138 

43:2436 
43.6142 
43.9870 

1.51974 
1.52118 
1.52262 

3.27418 
3.27729 
3.28039 

7.05400 
7.06070 
7.06738 

.284900 
.284091 
.283286 

3.54 
3.55 
3.56 

12.5316 
12.6025 
12.6736 

1.88149 
1.88414 
1.88680 

5.94979 
5.95819 
5.96657 

44.3619 
44.7389 
45.1180 

1.52406 
1.52549 
1.52692 

3.28348 
3.28657 
3.28965 

7.07404 
7.08070 
7.08734 

.282486 
.281690 
.280899 

3.57 
3.58 
3.59 

12.7449 
12.8164 

12.8881 

1.88944 
1.89209 

1.89473 

5.97495 
5.98331 
5.99166 

45.4993 

45.8827 
46.2683 

1.52835 
1.52978 
1.53120 

3.29273 
3.29580 
3.29887 

7.09397 
7.10059 
7.10719 

.280112 
.279330 

.278552 

3.60 

12.9800 

1.89737 

6.00000 

46.6560 

1.53262 

3.30193 

7.11379 

.277778 

3.61 
3.62 
3.63 

13.0321 
13.1044 
13.1769 

1.90000 
1.90263 
1.90526 

6.00833 
6.01664 
6.02495 

47.0459 
47.4379 
47.8321 

1.53404 
1.53545 
1.53686 

3.30498 
3.30803 
3.31107 

7.12037 
7.12694 
7.13349 

.277008 
.276243 
.275482 

3.64 
3.65 
3.66 

13.2496 
13.3225 
13.3956 

1.90788 
1.91050 
1.91311 

6.03324 
6.04152 
6.04979 

48.2285 
48.6271 
49.0279 

1.53827 
1.53968 
1.54109 

3.31411 
3.31714 
3.32017 

7.14004 
7.14657 
7.15309 

.274725 
.273973 
.273224 

3.67 
3.68 
3.69 

13.4689 
13.5424 
13.6161 

1.91572 
1.91833 
1.92094 

6.05805 
6.06630 
6.07454 

49.4309 
49.8360 
50.2434 

1.54249 
1.54389 
1.54529 

3.32319 
3.32621 
3.32922 

7.15960 
7.16610 
7.17258 

.272480 
.271739 
.271003 

3.70 

13.6900 

1.92354 

6.08276 

50.6530 

1.54668 

3.33222 

7.17905 

.270270 

3.71 
3.72 
3.73 

13.7641 
13.8384 
13.9129 

1.92614 
1.92873 
1.93132 

6.09098 
6.09918 
6.10737 

51.0648 
51.4788 
51.8951 

1.54807 
1.54946 
1.55085 

3.33522 
3.33822 
3.34120 

7.18552 
7.19197 
7.19840 

.269542 
.268817 
.263097 

3.74 
3.75 
3.76 

13.9876 
14.0625 
14.1376 

1.93391 
1.93649 
1.93907 

6.11555 
6.12372 
6.13188 

52.3136 
52.7344 
53.1574 

1.55223 
1.55362 
1.55500 

3.34419 
3.34716 
3.35014 

7.20483 
7.21125 
7.21765 

.267380 
.266667 
.265957 

3.77 
3.78 
3.79 

14.2129 
14.2884 
14.3641 

1.94165 
1.94422 
1.94679 

6.14003 
6.14817 
6.15630 

53.5826 
54.0102 
54.4399 

1.55637 
1.55775 
1.55912 

3.35310 
3.35607 
3.35902 

7.22405 
7.23043 
7.23680 

.265252 
.264550 
.263852 

3.80 

14.4400 

1.94936 

6.16441 

54.8720 

1.56049 

3.36198 

7.24316 

.263158 

3.81 
3.82 
3.83 

14.5161 
14.5924 
14.6689 

1.95192 
1.95448 
1.95704 

6.17252 
6.18061 
6.18870 

55.3063 
55.7430 
56.1819 

1.56186 
1.56322 
1.56459 

3.36492 
3.36786 
3.37080 

7.24950 
7.25584 
7.26217 

.262467 
.261780 
.261097 

3.84 
3.85 
3.86 

14.7456 
14.8225 
14.8996 

1.95959 
1.96214 
1.96469 

6.19677 
6.20484 
6.21289 

56.6231 
57.0666 
57.5125 

1.56595 
1.56731 
1.56866 

3.37373 
3.37666 
3.37958 

7.26848 
7.27479 
7.28108 

.260417 
.259740 
.259067 

3.87 
3.88 
3.89 

14.9769 
15.0544 
15.1321 

1.96723 
1.96977 
1.97231 

6.22093 
6.22896 
6.23699 

57.9606 
58.4111 
58.8639 

1.57001 
1.57137 
1.57271 

3.38249 
3.38540 
3.38831 

7.28736 
7.29363 
7.29989 

.258398 
.257732 
.257069 

3.90 

15.2100 

1.97484 

6.24500 

59.3190 

1.57406 

3.39121 

7.30614 

.256410 

3.91 
3.92 
3.93 

15.2881 
15.3664 
15.4449 

1.97737 
1.97990 
1.98242 

6.25300 
6.26099 
6.26897 

59.7765 
60.2363 
60.6985 

1.57541 
1.57675 
1.57809 

3.39411 
3.39700 
3.39988 

7.31238 
7.31861 
7.32483 

.255754 
.255102 
.254453 

3.94 
3.95 
3.96 

15.5236 
15.6025 
15.6816 

1.98494 
1.98746 
1.98997 

6.27694 
6.28490 
6.29285 

61.1630 
61.6299 
62.0991 

1.57942 
1.58076 
1.58209 

3.40277 
3.40564 
3.40851 

7.33104 
7.33723 
7.34342 

.253807 
.253165 
.252525 

3.97 
3.98 
3.99 

15.7609 
15.8404 
15.9201 

1.99249 
1.99499 
1.99750 

6.30079 
6.30872 
6.31664 

62.5708 
63.0448 
63.5212 

1.58342 
1.58475 
1.58608 

3.41138 
3.41424 
3.41710 

7.34960 
7.35576 
7.36192 

.251889 
.251256 

.250627 

4.00 

16.0000 

2.00000 

6.32456 

64.0000 

1.58740 

3.41995 

7.36806 

.250000 

n 

n2 

V^ 

VlO  n 

n3 

31  — 

Vrc 

^10^ 

\rLOO~^ 

1/n 

100 


Powers  —  Roots  —  Reciprocals 


[VI 


n 

n2 

Vn 

VIo^ 

n3 

Jn 

VlOn 

^100  n 

l/n 

4.00 

16.0000 

2.00000 

6.32456 

64.0000 

1.58740 

3.41995 

7.30806 

.250000 

4.01 
4.02 
4.03 

16.0801 
16.1604 
16.2409 

2.00250 
2.00499 
2.00749 

6.33246 
6.34035 
6.34823 

64.4812 
64.9648 
65.4508 

1.58872 
1.59004 
1.59136 

3.42280 
3.42564 
3.42848 

7.37420 
7.38032 
7.38644 

.249377 
.248756 
.248139 

4.04 
4.05 
4.06 

16.3216 
16.4025 
16.4836 

2.00998 
2.01246 
2.01494 

6.35610 
6.36396 
6.37181 

65.9393 
66.4301 
66.9234 

1.59267 
1.59399 
1.59530 

3.43131 
3.43414 
3.43697 

7.39254 
7.39864 
7.40472 

.247525 
.246914 
.246305 

4.07 
4.08 
4.09 

16.5649 
16.6464 
16.7281 

2.01742 
2.01990 
2.02237 

6.37966 
6.38749 
6.39531 

67.4191 
67.9173 
68.4179 

1.59661 
1.59791 
1.59922 

3.43979 
3.44260 
3.44541 

7.41080 
7.41686 
7.42291 

.245700 
.245098 
.244499 

4.10 

16.8100 

2.02485 

6.40312 

68.9210 

1.60052 

3.44822 

7.42896 

.243902 

4.11 
4.12 
4.13 

16.8921 
16.9744 
17.0569 

2.02731 
2.02978 
2.03224 

6.41093 
6.41872 
6.42651 

69.4265 
69.9345 
70.4450 

1.60182 
1.60312 
1.60441 

3.45102 
3.45382 
3.45661 

7.43499 
7.44102 
7.44703 

.243309 
.242718 
.242131 

4.14 
4.15 
4.16 

17.1396 
17.2225 
17.3056 

2.03470 
2.03715 
2.03961 

6.43428 
6.44205 
6.44981 

70.9579 
71.4734 
71.9913 

1.60571 
1.60700 
1.60829 

3.45939 

3.4G218 
3.46496 

7.45304 
7.45904 
7.46502 

.241546 
.240964 
.240385 

4.17 
4.18 
4.19 

17.3889 
17.4724 
17.5561 

2.04206 
2.04450 
2.04695 

6.45755 
6.46529 
6.47302 

72.5117 
73.0346 
73.5601 

1.60958 
1.61086 
1.61215 

3.46773 
3.47050 
3.47327 

7.47100 
7.47697 
7.48292 

.239808 
.239234 
.238663 

4.20 

17.6400 

2.04939 

6.48074 

74.0880 

1.61343 

3.47603 

7.48887 

.238095 

4.21 
4.22 
4.23 

17.7241 
17.8084 
17.8929 

2.05183 
2.05426 
2.05670 

6.48845 
6.49615 
6.50384 

74.6185 
75.1514 
75.6870 

1.61471 
1.61599 
1.61726 

3.47878 
3.48154 
3.48428 

7.49481 
7.50074 
7.50666 

.237530 
.236967 
.236407 

4.24 
4.25 
4.26 

17.9776 
18.0625 
18.1476 

2.05913 
2.06155 
2.06398 

6.51153 
6.51920 
6.52687 

76.2250 
76.7656 
77.3088 

1.61853 
1.61981 
1.62108 

3.48703 
3.48977 
3.49250 

7.51257 
7.51847 
7.52437 

.235849 
.235294 
.234742 

4.27 
4.28 
4.29 

18.2329 
18.3184 
18.4041 

2.06640 
2.06882 
2.07123 

6.53452 
6.54217 
6.54981 

77.8545 
78.4028 
78.9536 

1.62234 
1.62361 

1.62487 

3.49523 
3.49796 
3.50068 

7.53025 
7.53612 
7.54199 

.234192 
.233645 
.233100 

4.30 

18.4900 

2.07364 

6.55744 

79.5070 

1.62613 

3.50340 

7.54784 

.232558 

4.31 
4.32 
4.33 

18.5761 
18.6624 
18.7489 

2.07605 
2.07846 
2.08087 

6.56506 
6.57267 
6.58027 

80.0630 
80.6216 
81.1827 

1.62739 
1.62865 
1.62991 

3.50611 
3.50882 
3.51153 

7.55369 
7.55953 
7.56535 

.232019 
.231481 
.230947 

4.34 
4.35 
4.36 

18.8356 
18.9225 
19.0096 

2.08327 
2.08567 
2.08806 

6.58787 
6.59545 
6.60303 

81.7465 
82.3129 
82.8819 

1.63116 
1.63241 
1.63366 

3.51423 

3.51692 
3.51962 

7.57117 
7.57698 
7.58279 

.230415 

.229885 
.229358 

4.37 
4.38 
4.39 

19.0969 
19.1844 
19.2721 

2.09045 
2.09284 
2.09523 

6.61060 
6.61816 
6.62571 

83.4535 
84.0277 
84.6045 

1.63491 
1.63619 
1.63740 

3.52231 
3.52499 
3.52767 

7.58858 
7.59436 
7.60014 

.228833 
.228311 
.227790 

4.40 

19.3600 

2.09762 

6.63325 

85.1840 

1.63864 

3.53035 

7.60590 

.227273 

4.41 
4.42 
4.43 

19.4481 
19.5364 
19.6249 

2.10000 
2.10238 
2.10476 

6.64078 
6.64831 
6.65582 

85.7661 
86.3509 
86.9383 

1.63988 
1.64112 
1.64236 

3.53302 
3.53569 
3.53835 

7.61166 
7.61741 
7.62315 

.226757 
.226244 
.225734 

4.44 
4.45 
4.46 

19.7136 
19.8025 
19.8916 

2.10713 
2.10950 
2.11187 

6.66333 
6.67083 
6.67832 

87.5284 
88.1211 
88.7165 

1.64359 
1.64483 
1.64606 

3.54101 
3.54367 
3.54632 

7.62888 
7.63461 
7.64032 

.225225 
.224719 
.224215 

4.47 
4.48 
4.49 

19.9809 
20.0704 
20.1001 

2.11424 
2.11660 
2.11896 

6.68581 
6.69328 
6.70075 

89.3146 
89.9154 
90.5188 

1.64729 
1.64851 
1.64974 

3.54897 
3.55162 
3.55426 

7.64603 
7.65172 
7.65741 

.223714 
.223214 
.222717 

4.50 

20.2500 

2.12132 

6.70820 

91.1250 

1.65096 

3.55689 

7.66309 

.222222 

71 

/I2 

V^ 

VlOn 

n3 

31  — 

Vn 

^ToTi 

\Too~^ 

l/n 

VI] 


Powers  —  Roots  —  Reciprocals 


101 


n 

n2 

V^ 

\IolI 

n3 

^n 

\!0n 

^100  n 

1/n 

4.50 

20.2500 

2.12132 

6.70S20 

91.1250 

1.65096 

3.55689 

7.66309 

.222222 

4.51 
4.52 
4.53 

20.3401 
20.4304 
20.5209 

2.12368 
2.12603 
2.12838 

6.71565 
6.72309 
6.73053 

91.7339 
92.3454 
92.9597 

1.65219 
1.65341 
1.65462 

3.55953 
3.56215 
3.56478 

7.66877 
7.67443 
7.68009 

.221729 
.221239 
.220751 

4.54 
4.55 
4.56 

20.6116 
20.7025 
20.7936 

2.13073 
2.13307 
2.13542 

6.73795 

6.74537 
6.75278 

93.5767 
94.1964 
94.8188 

1.65584 
1.65706 
1.65827 

3.56740 
3.57002 
3.57263 

7.68573 
7.69137 
7.69700 

.220264 
.219780 
.219298 

4.57 
4.58 
4.59 

20.8849 
20.9764 
21.0681 

2.13776 
2.14009 
2.14243 

6.76018 
6.76757 
6.77495 

95.4440 
96.0719 
96.7026 

1.65948 
1.66069 
1.66190 

3.57524 
3.57785 
3.58045 

7.70262 
7.70824 
7.71384 

.218818 
.218341 
.217865 

4.60 

21.1600 

2.14476 

6.78233 

97.3360 

1.66310 

3.58305 

7.71944 

.217391 

4.61 
4.62 
4.63 

21.2521 
21.3444 
21.4369 

2.14709 
2.14942 
2.15174 

6.78970 
6.79706 
6.80441 

97.9722 
98.6111 
99.2528 

1.66431 
1.66551 
1.66671 

3.58564 
3.58823 
3.59082 

7.72503 
7.73061 
7.73619 

.216920 
.216450 
.215983 

4.64 
4.65 
4.66 

21.5296 
21.6225 
21.7156 

2.15407 
2.15639 
2.15870 

6.81175 
6.81909 
6.82642 

99.8973 
100.545 
101.195 

1.66791 
1.66911 
1.67030 

3.59340 
3.59598 
3.59856 

7.74175 
7.74731 
7.75286 

.215517 
.215054 
.214592 

4.67 
4.68 
4.69 

21.8089 
21.9024 
21.9961 

2.16102 
2.16333 
2.16564 

6.83374 
6.84105 
6.84836 

101.848 
102.503 
103.162 

1.67150 
1.67269 
1.67388 

3.60113 
3.60370 
3.60626 

7.75840 
7.76394 
7.76946 

.214133 
.213675 
.213220 

4.70 

22.0900 

2.16795 

6.85565 

103.823 

1.67507 

3.60883 

7.77498 

.212766 

4.71 
4.72 
4.73 

22.1841 
22.2784 
22.3729 

2.17025 
2.17256 
2.17486 

6.86294 
6.87023 
6.87750 

]  04.487 
105.154 
105.824 

1.67626 
1.67744 
1.67863 

3.61138 
3.61394 
3.61649 

7.78049 
7.78599 
7.79149 

.212314 
.211864 
.211416 

4.74 
4.75 
4.76 

22.4676 
22.5625 
22.6576 

2.17715 
2.17945 

2.18174 

6.88477 
6.89202 
6.89928 

106.496 
107.172 
107.850 

1.67981 
1.68099 
1.68217 

3.61903 
3.62158 
3.62412 

7.79697 
7.80245 
7.80793 

.210970 
.210526 
.210084 

4.77 
4.78 
4.79 

22.7529 
22.8484 
22.9441 

2.18403 
2.18632 
2.18861 

6.90652 
6.91375 
6.92098 

108.531 
109.215 
109.902 

1.68334 
1.68452 
1.68569 

3.62665 
3.62919 
3.63172 

7.81339 

7.81885 
7.82429 

.209644 
.209205 

.208768 

4.80 

23.0400 

2.19089 

6.92820 

110.592 

1.68687 

3.63424 

7.82974 

.208333 

4.81 
4.82 
4.83 

23.1361 
23.2324 
23.3289 

2.19317 
2.19545 
2.19773 

6.93542 
6.94262 
6.94982 

111.285 
111.980 
112.679 

1.68804 
1.68920 
1.69037 

3.63676 
3.63928 
3.64180 

7.83517 
7.84059 
7.84601 

.207900 
.207469 
.207039 

4.84 
4.85 
4.86 

23.4256 
23.5225 
23.6196 

2.20000 
2.20227 
2.20454 

6.95701 
6.96419 
6.97137 

113.380 
114.084 
114.791 

1.69154 
1.69270 
1.69386 

3.64431 
3.64682 
3.64932 

7.85142 
7.85683 
7.86222 

.206612 
.206186 
.205761 

4.87 
4.88 
4.89 

23.7169 
23.8144 
23.9121 

2.20681 
2.20907 
2.21133 

6.97854 
6.98570 
6.99285 

115.501 
116.214 
116.930 

1.69503 
1.69619 
1.69734 

3.65182 
3.65432 
3.65681 

7.86761 

7.87299 
7.87837 

.205339 
.204918 
.204499 

4.90 

24.0100 

2.21359 

7.00000 

117.649 

1.69850 

3.65931 

7.88374 

.204082 

4.91 
4.92 
4.93 

24.1081 
24.2064 
24.3049 

2.21585 
2.21811 
2.22036 

7.00714 
7.01427 
7.02140 

118.371 
119.095 
119.823 

1.69965 
1.70081 
1.70196 

3.66179 
3.66428 
3.66676 

7.88909 
7.89445 
7.89979 

.203666 
.203252 
.202840 

4.94 
4.95 
4.96 

24.4036 
24.5025 
24.6016 

2.22261 
2.22486 
2.22711 

7.02851 
7.03562 
7.04273 

120.554 
121.287 
122.024 

1.70311 
1.70426 
1.70540 

3.66924 
3.67171 
3.67418 

7.90513 
7.91046 
7.91578 

.202429 
.202020 
.201613 

4.97 
4.98 
4.99 

24.7009 
24.8004 
24.9001 

2.22935 
2.23159 
2.23383 

7.04982 
7.05691 
7.06399 

122.763 
123.506 
124.251 

1.70655 
1.70769 
1.70884 

3.67665 
3.67911 
3.68157 

7.92110 
7.92641 
7.93171 

.201207 
.200803 
.200401 

5.00 

25.0000 

2.23607 

7.07107 

125.000 

1.70998 

3.68403 

7.93701 

.200000 

n 

n2 

Vn 

AloTI 

nj 

31  — 

Vn 

\1oTI 

xlOO  n 

1/n 

102 


Powers  —  Roots  —  Reciprocals 


[VI 


n 

n2 

V» 

VlOn 

n3 

31  — 

Vn 

^ToTl 

S^IOO  /I 

l/n 

5.00 

25.0000 

2.23607 

7.07107 

125.000 

1.70998 

3.68403 

7.93701 

.200000 

5.01 
5.02 
5.03 

25.1001 
25.2004 
25.3009 

2.23830 
2.24054 
2.24277 

7.07814 
7.08520 
7.09225 

125.752 
126.506 
127.264 

1.71112 
1.71225 
1.71339 

3.68649 
3.68894 
3.69138 

7.94229 
7.94757 
7.95285 

.199601 
.199203 
.198807 

5.04 
5.05 
5.06 

25.4016 
25.5025 
25.6036 

2.24499 
2.24722 
2.24944 

7.09930 
7.10634 
7.11337 

128.024 
128.788 
129.554 

1.71452 
1.71566 
1.71679 

3.69383 
3.69627 
3.69871 

7.95811 
7.96337 
7.96863 

.198413 
.198020 
.197628 

5.07 
5.08 
5.09 

25.7049 
25.8064 
25.9081 

2.25167 
2.25389 
2.25610 

7.12039 
7.12741 
7.13442 

130.324 
131.097 
131.872 

1.71792 
1.71905 
1.72017 

3.70114 
3.70357 
3.70600 

7.97387 
7.97911 

7.98434 

.197239 
.196850 
.196464 

5.10 

26.0100 

2.25832 

7.14143 

132.651 

1.72130 

3.70843 

7.98957 

.196078 

5.11 
5.12 
5.13 

26.1121 
26.2144 
26.3169 

2.26053 
2.26274 
2.26495 

7.14843 
7.15542 
7.16240 

133.433 
134.218 
135.006 

1.72242 
1.72355 
1.72467 

3.71085 
3.71327 
3.71569 

7.99479 
8.00000 
8.00520 

.195695 
.195312 
.194932 

5.14 
5.15 
5.16 

26.4196 
26.5225 
26.6256 

2.26716 
2.26936 
2.27156 

7.16938 
7.17635 
7.18331 

135.797 
136.591 
137.388 

1.72579 
1.72691 
1.72802 

3.71810 
3.72051 
3.72292 

8.01040 
8.01559 
8.02078 

.194553 
.194175 
.193798 

5.17 
5.18 
5.19 

26.7289 
26.8324 
26.9361 

2.27376 
2.27596 
2.27816 

7.19027 
7.19722 
7.20417 

138.188 
138.992 
139.798 

1.72914 
1.73025 
1.73137 

3.72532 
3.72772 
3.73012 

8.02596 
8.03113 
8.03629 

.193424 
.193050 
.192678 

5.20 

27.0400 

2.28035 

7.21110 

140.608 

1.73248 

3.73251 

8.04145 

.192308 

5.21 
5.22 
5.23 

27.1441 
27.2484 
27.3529 

2.28254 
2.28473 
2.28692 

7.21803 
7.22496 
7.23187 

141.421 
142.237 
143.056 

1.73359 
1.73470 
1.73580 

3.73490 
3.73729 
3.73968 

8.04660 
8.05175 
8.05689 

.191939 
.191571 
.191205 

5.24 
5.25 
5.26 

27.4576 
27.5625 
27.6676 

2.28910 
2.29129 
2.29347 

7.23878 
7.24569 
7.25259 

143.878 
144.703 
145.532 

1.73691 
1.73801 
1.73912 

3.74206 
3.74443 
3.74681 

8.06202 
8.06714 
8.07226 

.190840 
.190476 
.190114 

5.27 

5.28 
5.29 

27.7729 
27.8784 
27.9841 

2.29565 
2.29783 
2.30000 

7.25948 
7.26636 
7.27324 

146.363 
147.198 
148.036 

1.74022 
1.74132 
1.74242 

3.74918 
3.75155 
3.75392 

8.07737 
8.08248 
8.08758 

.189753 
.189394 
.189036 

5.30 

28.0900 

2.30217 

7.28011 

148.877 

1.74351 

3.75629 

8.09267 

.188679 

5.31 
5.32 
5.33 

28.1961 
28.3024 
28.4089 

2.30434 
2.30651 
2.30868 

7.28697 
7.29383 
7.30068 

149.721 
150.569 
151.419 

1.74461 
1.74570 
1.74680 

3.75865 
3.76101 
3.76336 

8.09776 
8.10284 
8.10791 

.188324 
.187970 
.187617 

5.34 
5.35 
5.36 

28.5156 
28.6225 
28.7296 

2.31084 
2.31301 
2.31517 

7.30753 
7.31437 
7.32120 

152.273 
153.130 
153.991 

1.74789 
1.74898 
1.75007 

3.76571 
3.76806 
3.77041 

8.11298 
8.11804 
8.12310 

.187266 
.186916 
.186567 

5.37 
5.38 
5.39 

28.8369 
28.9444 
29.0521 

2.31733 
2.31948 
2.32164 

7.32803 
7.33485 
7.34166 

154.854 
155.721 
156.591 

1.75116 
1.75224 
1.75333 

3.77275 
3.77509 
3.77743 

8.12814 
8.13319 

8.13822 

.186220 
.185874 
.185529 

5.40 

29.1600 

2.32379 

7.34847 

157.464 

1.75441 

3.77976 

8.14325 

.185185 

5.41 
5.42 
5.43 

29.2681 
29.3764 
29.4849 

2.32594 
2.32809 
2.33024 

7.35527 
7.36206 
7.36885 

158.340 
159.220 
160.103 

1.75549 
1.75657 
1.75765 

3.78209 
3.78442 
3.78675 

8.14828 
8.15329 
8.15831 

.184843 
.184502 
.184162 

5.44 
5.45 
5.46 

29.5936 
29.7025 
29.8116 

2.33238 
2.33452 
2.33666 

7.37564 
7.38241 
7.38918 

160.989 
161.879 
162.771 

1.75873 
1.75981 
1.76088 

3.78907 
3.79139 
3.79371 

8.16331 
8.16831 
8.17330 

.183824 
.183486 
.183150 

5.47 
5.48 
5.49 

29.9209 
30.0304 
30.1401 

2.33880 
2.34094 
2.34307 

7.39594 

7.40270 
7.40945 

163.667 

164.567 
165.469 

1.76196 
1.76303 
1.76410 

3.79603 
3.79834 
3.80065 

8.17829 
8.18327 

8.18824 

.182815 
.182482 
.182149 

5.50 

30.2500 

2.34521 

7.41620 

166.375 

1.76517 

3.80295 

8.19321 

.181818 

n 

n2 

V^ 

VTo~rT 

n3 

3/  — 
Vn 

1/WTi 

ShOO  n 

l/n 

VI] 


Powers  —  Roots  —  Reciprocals 


103 


n 

n2 

^ 

VlO  n 

n3 

31  

\n 

\  10  n 

^100  n 

l/n 

5.50 

30.2500 

2.34521 

7.41620 

166.375 

1.76517 

3.80295 

8.19321 

.181818 

5.51 
5.52 
5.53 

30.3601 
30.4704 
30.5809 

2.34734 
2.34947 
2.35160 

7.42294 
7.42967 
7.43640 

167.284 
168.197 
169.112 

1.76624 
1.76731 
1.76838 

3.80526 
3.80756 
3.80985 

8.19818 
8.20313 
8.20808 

.181488 
.181159 
.180832 

5.54 
5.55 
5.56 

30.6916 
30.8025 
30.9136 

2.35372 
2.35584 
2.35797 

7.44312 
7.44983 
7.45654 

170.031 
170.954 
171.880 

1.76944 
1.77051 
1.77157 

3.81215 
3.81444 
3.81673 

8.21303 
8.21797 
8.22290 

.180505 
.180180 
.179856 

5.57 
5.58 
5.59 

31.0249 
31.1364 
31.2481 

2.36008 
2.36220 
2.36432 

7.46324 
7.46994 
7.47663 

172.809 
173.741 
174.677 

1.77263 
1.77369 
1.77475 

3.81902 
3.82130 
3.82358 

8.22783 
8.23275 
8.23766 

.179533 
.179211 
.178891 

5.60 

31.3600 

2.36643 

7.48331 

175.616 

1.77581 

3.82586 

8.24257 

.178571 

5.61 
5.62 
5.63 

31.4721 
31.5844 
31.6969 

2.36854 
2.37065 
2.37276 

7.48999 
7.49667 
7.50333 

176.558 
177.504 
178.454 

1.77686 
1.77792 
1.77897 

3.82814 
3.83041 
3.83268 

8.24747 
8.25237 
8.25726 

.178253 
.177936 
.177620 

5.64 
5.65 
5.66 

31.8096 
31.9225 
32.0356 

2.37487 
2.37697 
2.37908 

7.50999 
7.51665 
7.52330 

179.406 
180.362 
181.321 

1.78003 
1.78108 
1.78213 

3.83495 
3.83722 
3.83948 

8.26215 
8.26703 
8.27190 

.177305 
.176991 
.176678 

5.67 
5.68 
5.69 

32.1489 
32.2624 
32.3761 

2.38118 
2.38328 
2.38537 

7.52994 
7.53658 
7.54321 

182.284 
183.250 
184.220 

1.78318 
1.78422 
1.78527 

3.84174 
3.<M399 
3.84625 

8.27677 
8.28164 
8.28649 

.176367 
.176056 
.175747 

5.70 

32.4900 

2.38747 

7.54983 

185.193 

1.78632 

3.84850 

8.29134 

.175439 

5.71 
5.72 
5.73 

32.6041 
32.7184 
32.8329 

2.38956 
2.39165 
2.39374 

7.55645 
7.56307 
7.56968 

186.169 
187.149 
188.133 

1.78736 
1.78840 
1.78944 

3.85075 
3.85300 
3.85524 

8.29619 
8.30103 
8.30587 

.175131 
.174825 
.174520 

5.74 
5.75 
5.76 

32.9476 
33.0625 
33.1776 

2.39583 
2.39792 
2.40000 

7.57628 
7.58288 
7.58947 

189.119 
190.109 
191.103 

1.79048 
1.79152 
1.79256 

3.85748 
3.85972 
3.86196 

8.31069 
8.31552 
8.32034 

.174216 
.173913 
.173611 

5.77 
5.78 
5.79 

33.2929 
33.4084 
33.5241 

2.40208 
2.40416 
2.40624 

7.59605 
7.60263 
7.60920 

192.100 
193.101 
194.105 

1.79360 
1.79463 
1.79567 

3.86419 
3.86642 
3.86865 

8.32515 
8.32995 
8.33476 

.173310 
.173010 
.172712 

5.80 

33.6400 

2.40832 

7.61577 

195.112 

1.79670 

3.87088 

8.33955 

.172414 

5.81 
5.82 
5.83 

33.7561 
33.8724 
33.9889 

2.41039 
2.41247 
2.41454 

7.62234 
7.62889 
7.63544 

196.123 
197.137 
198.155 

1.79773 
1.79876 
1.79979 

3.87310 
3.87532 
3.87754 

8.34434 
8.34913 
8.35390 

.172117 
.171821 
.171527 

5.84 
5.85 
5.86 

34.1056 
34.2225 
34.3396 

2.41661 
2.41868 
2.42074 

7.64199 
7.64853 
7.65506 

199.177 
200.202 
201.230 

1.80082 
1.80185 
1.80288 

3.87975 
3.88197 
3.88418 

8.35868 
8.36345 
8.36821 

.171233 
.170940 
.170649 

5.87 
5.88 
5.89 

34.4569 
34.5744 
34.6921 

2.42281 
2.42487 
2.42693 

7.66159 
7.66812 
7.67463 

202.262 
203.297 
204.336 

1.80390 
1.80492 
1.80595 

3.88639 
3.88859 
3.89080 

8.37297 
8.37772 
8.38247 

.170358 
.170068 
.169779 

5.90 

34.8100 

2.42899 

7.68115 

205.379 

1.80697 

3.89300 

8.38721 

.169492 

5.91 
5.92 
5.93 

34.9281 
35.0464 
35.1649 

2.43105 
2.43311 
2.43516 

7.68765 
7.69415 
7.70065 

206.425 
207.475 
208.528 

1.80799 
1.80901 
1.81003 

3.89519 
3.89739 
3.89958 

8.39194 
8.39667 
8.40140 

.169205 
.168919 
.168634 

5.94 
5.95 
5.96 

35.2836 
35.4025 
35.5216 

2.43721 
2.43926 
2.44131 

7.70714 
7.71362 
7.72010 

209.585 
210.645 
211.709 

1.81104 
1.81206 
1.81307 

3.90177 
3.90396 
3.90615 

8.40612 
8.41083 
8.41554 

.168350 
.168067 
.167785 

5.97 
5.98 
5.99 

35.6409 
35.7604 
35.8801 

2.44336 
2.44540 

2.44745 

7.72658 
7.73305 
7.73951 

212.776 
213.847 
214.922 

1.81409 
1.81510 
1.81611 

3.90833 
3.91051 
3.91269 

8.42025 
8.42494 
8.42964 

.167504 
.167224 
.166945 

6.00 

36.0000 

2.44949 

7.74597 

216.000 

1.81712 

3.91487 

8.43433 

.166667 

n 

n2 

V^ 

VlO  71 

n3 

££ 

jfWli 

^iwTTr 

l/n 

104 


Powers  —  Roots  —  Reciprocals 


[VI 


n 

n2 

V^ 

VlOn 

n3 

3/  — 

Vn 

3w7i 

^100  n 

1/n 

6.00 

36.0000 

2.44949 

7.74597 

216.000 

1.81712 

3.91487 

8.43433 

.166667 

6.01 
6.02 
6.03 

36.1201 
36.2404 
36.3609 

2.45153 
2.45357 
2.45561 

7.75242 
7.75887 
7.76531 

217.082 
218.167 
219.256 

1.81813 
1.81914 
1.82014 

3.91704 
3.91921 
3.92138 

8.43901 
8.44369 
8.44836 

.166389 
.166113 
.165837 

6.04 
6.05 
6.06 

36.4816 
36.6025 
36.7236 

2.45764 
2.45967 
2.46171 

7.77174 
7.77817 
7.78460 

220.349 
221.445 
222.545 

1.82115 
1.82215 
1.82316 

3.92355 
3.92571 
3.92787 

8.45303 
8.45769 
8.46235 

.165563 
.165289 
.165017 

6.07 
6.08 
6.09 

36.8449 
36.9664 
37.0881 

2.46374 
2.46577 
2.46779 

7.79102 
7.79744 
7.80385 

223.649 
224.756 
225.867 

1.82416 
1.82516 
1.82616 

3.93003 
3.93219 
3.93434 

8.46700 
8.47165 
8.47629 

.164745 
.164474 
.164204 

6.10 

37.2100 

2.46982 

7.81025 

226.981 

1.82716 

3.93650 

8.48093 

.163934 

6.11 
6.12 
6.13 

37.3321 
37.4544 
37.5769 

2.47184 
2.47386 
2.47588 

7.81665 
7.82304 
7.82943 

228.099 
229.221 
230.346 

1.82816 
1.82915 
1.83015 

3.93865 
3.94079 
3.94294 

8.48556 
8.49018 
8.49481 

.163666 
.163399 
.163132 

6.14 
6.15 
6.16 

37.6996 
37.8225 
37.9456 

2.47790 
2.47992 
2.48193 

7.83582 
7.84219 
7.84857 

231.476 
232.608 
233.745 

1.83115 
1.83214 
1.83313 

3.94508 
3.94722 
3.94936 

8.49942 
8.50403 
8.50864 

.162866 
.162602 
.162338 

6.17 
6.18 
6.19 

38.0689 
38.1924 
38.3161 

2.48395 
2.48596 
2.48797 

7.85493 
7.86130 
7.86766 

234.885 
236.029 
237.177 

1.83412 
1.83511 
1.83610 

3.95150 
3.95363 
3.95576 

8.51324 
8.51784 
8.52243 

.162075 
.161812 
.161551 

6.20 

38.4400 

2.48998 

7.87401 

238.328 

1.83709 

3.95789 

8.52702 

.161290 

6.21 
6.22 
6.23 

38.5641 
38.6884 
38.8129 

2.49199 
2.49399 
2.49600 

7.88036 
7.88670 
7.89303 

239.483 
240.642 
241.804 

1.83808 
1.83906 
1.84005 

3.96002 
3.96214 
3.96427 

8.53160 
8.53618 
8.54075 

.161031 
.160772 
.160514 

6.24 
6.25 
6.26 

38.9376 
39.0625 
39.1876 

2.49800 
2.50000 
2.50200 

7.89937 
7.90569 
7.91202 

242.971 
244.141 
245.314 

1.84103 
1.84202 
1.84300 

3.96638 
3.96850 
3.97062 

8.54532 

8.54988 
8.55444 

.160256 
.160000 
.159744 

6.27 
6.28 
6.29 

39.3129 
39.4384 
39.5641 

2.50400 
2.50599 
2.50799 

7.91833 
7.92465 
7.93095 

246.492 
247.673 

248.858 

1.84398 
1.84496 
1.84594 

3.97273 
3.97484 
3.97695 

8.55899 
8.56354 
8.56808 

.159490 
.159236 

.158983 

6.30 

39.6900 

2.50998 

7.93725 

250.047 

1.84691 

3.97906 

8.57262 

.158730 

6.31 
6.32 
6.33 

39.8161 
39.9424 
40.0689 

2.51197 
2.51396 
2.51595 

7.94355 
7.94984 
7.95613 

251.240 
252.436 
253.636 

1.84789 
1.84887 
1.84984 

3.98116 
3.98326 
3.98536 

8.57715 
8.58168 
8.58620 

.158479 
.158228 
.157978 

6.34 
6.35 
6.36 

40.1956 
40.3225 
40.4496 

2.51794 
2.51992 
2.52190 

7.96241 
7.96869 
7.97496 

254.840 
256.048 
257.259 

1.85082 
1.85179 
1.85276 

3.98746 
3.98956 
3.99165 

8.59072 
8.59524 
8.59975 

.157729 
.157480 
.157233 

6.37 
6.38 
6.39 

40.5769 
40.7044 
40.8321 

2.52389 
2.52587 

2.52784 

7.98123 
7.98749 
7.99375 

258.475 
259.694 
260.917 

1.85373 
1.85470 
1.85567 

3.99374 
3.99583 
3.99792 

8.60425 
8.60875 
8.61325 

.156986 
.156740 
.156495 

6.40 

40.9600 

2.52982 

8.00000 

262.144 

1.85664 

4.00000 

8.61774 

.156250 

6.41 
6.42 
6.43 

41.0881 
41.2164 
41.3449 

2.53180 
2.53377 
2.53574 

8.00625 
8.01249 
8.01873 

263.375 
264.609 
265.848 

1.85760 
1.85857 
1.85953 

4.00208 
4.00416 
4.00624 

8.62222 
8.62671 
8.63118 

.156006 
.155763 
.155521 

6.44 
6.45 
6.46 

41.4736 
41.6025 
41.7316 

2.53772 
2.53969 
2.54165 

8.02496 
8.03119 
8.03741 

267.090 
268.336 
269.586 

1.86050 
1.86146 
1.86242 

4.00832 
4.01039 
4.01246 

8.63566 
8.64012 
8.64459 

.155280 
.155039 
.154799 

6.47 
6.48 
6.49 

41.8609 
41.9904 
42.1201 

2.54362 
2.54558 
2.54755 

8.04363 
8.04984 
8.05605 

270.840 
272.098 
273.359 

1.86338 
1.86434 
1.86530 

4.01453 
4.01660 
4.01866 

8.64904 
8.65350 
8.65795 

.154560 
.154321 
.154083 

6.50 

42.2500 

2.54951 

8.06226 

274.625 

1.86626 

4.02073 

8.66239 

.153846 

n 

H2 

V^ 

VIoTi 

n3 

31  — 

Vn 

^Io7^ 

^locTn" 

1/n 

Powers  —  Roots  —  Reciprocals 


105 


n 

n2 

V^ 

VIoTI 

n3 

fn 

^Io7i 

j/Twll 

1/n 

6.50 

42.2500 

2.54951 

8.06226 

274.625 

1.86626 

4.02073 

8.66239 

.153846 

6.51 
6.52 
6.53 

42.3801 
42.5104 
42.6409 

2.55147 
2.55343 
2.55539 

8.06846 
8.07465 
8.08084 

275.894 
277.168 
278.445 

1.86721 
1.86817 
1.86912 

4.02279 
4.02485 
4.02690 

8.66683 
8.67127 
8.67570 

.153610 
.153374 
.153139 

6.54 
6.55 
6.56 

42.7716 
42.9025 
43.0336 

2.55734 
2.55930 
2.56125 

8.08703 
8.09321 
8.09938 

279.726 
281.011 
282.300 

1.87008 
1.87103 
1.87198 

4.02896 
4.03101 
4.03306 

8.68012 
8.68455 
8.68896 

.152905 
.152672 
.152439 

6.57 
6.58 
6.59 

43.1649 
43.2964 
43.4281 

2.56320 
2.56515 
2.56710 

8.10555 
8.11172 

8.11788 

283.593 
284.890 
286.191 

1.87293 
1.87388 
1.87483 

4.03511 
4.03715 
4.03920 

8.69338 
8.69778 
8.70219 

.152207 
.151976 
.151745 

6.60 

43.5600 

2.56905 

8.12404 

287.496 

1.87578 

4.04124 

8.70659 

.151515 

6.61 
6.62 
6.63 

43.6921 
43.8244 
43.9569 

2.57099 
2.57294 

2.57488 

8.13019 
8.13634 
8.14248 

288.805 
290.118 
291.434 

1.87672 
1.87767 
1.87862 

4.04328 
4.04532 
4.04735 

8.71098 
8.71537 
8.71976 

.151286 
.151057 
.150830 

6.64 
6.65 
6.66 

44.0896 
44.2225 
44.3556 

2.57682 
2.57876 
2.58070 

8.14862 
8.15475 
8.16088 

292.755 
294.080 
295.408 

1.87956 
1.88050 
1.88144 

4.04939 
4.05142 
4.05345 

8.72414 
8.72852 
8.73289 

.150602 
.150376 
.150150 

6.67 
6.68 
6.69 

44.4889 
44.6224 
44.7561 

2.58263 
2.58457 
2.58650 

8.16701 
8.17313 
8.17924 

296.741 
298.078 
299.418 

1.88239 
1.88333 

1.88427 

4.05548 
4.05750 
4.05953 

8.73726 
8.74162 
8.74598 

.149925 
.149701 
.149477 

6.70 

44.8900 

2.58844 

8.18535 

300.763 

1.8S520 

4.06155 

8.75034 

.149254 

6.71 
6.72 
6.73 

45.0241 
45.1584 
45.2929 

2.59037 
2.59230 
2.59422 

8.19146 
8.19756 
8.20366 

302.112 
303.464 
304.821 

1.88614 
1.88708 
1.88801 

4.06357 
4.06559 
4.06760 

8.75469 
8.75904 
8.76338 

.149031 
.148810 
.148588 

6.74 
6.75 
6.76 

45.4276 
45.5625 
45.6976 

2.59615 
2.59808 
2.60000 

8.20975 
8.21584 
8.22192 

306.182 
307.547 
308.916 

1.88895 
1.88988 
1.89081 

4.06961 
4.07163 
4.07364 

8.76772 
8.77205 
8.77638 

.148368 
.148148 
.147929 

6.77 
6.78 
6.79 

45.8329 
45.9684 
46.1041 

2.60192 
2.60384 
2.60576 

8.22800 
8.23408 
8.24015 

310.289 
311.666 
313.047 

1.89175 
1.89268 
1.89361 

4.07564 
4.07765 
4.07965 

8.78071 
8.78503 
8.78935 

.147710 
.147493 
.147275 

6.80 

46.2400 

2.60768 

8.24621 

314.432 

1.89454 

4.08166 

8.79366 

.147059 

6.81 
6.82 
6.83 

46.3761 
46.5124 
46.6489 

2.60960 
2.61151 
2.61343 

8.25227 
8.25833 
8.26438 

315.821 
317.215 
318.612 

1.89546 
1.89639 
1.89732 

4.08365 
4.08565 
4.08765 

8.79797 
8.80227 
8.80657 

.146843 
.146628 
.146413 

6.84 
6.85 
6.86 

46.7856 
46.9225 
47.0596 

2.61534 
2.61725 
2.61916 

8.27043 
8.27647 
8.28251 

320.014 
321.419 
322.829 

1.89824 
1.89917 
1.90009 

4.08964 
4.09163 
4.09362 

8.81087 
8.81516 
8.81945 

.146199 
.145985 
.145773 

6.87 
6.88 
6.89 

47.1969 
47.3344 
47.4721 

2.62107 
2.62298 

2.62488 

8.28855 
8.29458 
8.30060 

324.243 
325.661 
327.083 

1.90102 
1.90194 
1.90286 

4.09561 
4.09760 
4.09958 

8.82373 
8.82801 
8.83228 

.145560 
.145349 
.145138 

6.90 

47.6100 

2.62679 

8.30662 

328.509 

1.90378 

4.10157 

8.83656 

.144928 

6.91 
6.92 
6.93 

47.7481 
47.8864 
48.0249 

2.62869 
2.63059 
2.63249 

8.31264 
8.31865 
8.32466 

329.939 
331.374 
332.813 

1.90470 
1.90562 
1.90653 

4.10355 
4.10552 
4.10750 

8.84082 
8.84509 
8.84934 

.144718 
.144509 
.144300 

6.94 
6.95 
6.96 

48.1636 
48.3025 
48.4416 

2.63439 
2.63629 
2.63818 

8.33067 
8.33667 
8.34266 

334.255 
335.702 
337.154 

1.90745 
1.90837 
1.90928 

4.10948 
4.11145 
4.11342 

8.85360 
8.85785 
8.86210 

.144092 
.143885 
.143678 

6.97 

6.98 
6.99 

48.5809 
48.7204 
48.8601 

2.64008 
2.64197 
2.64386 

8.34865 
8.35464 
8.36062 

338.609 
340.068 
341.532 

1.91019 
1.91111 
1.91202 

4.11539 
4.11736 
4.11932 

8.86634 
8.87058 
8.87481 

.143472 
.143266 
.143062 

7.00 

•19.0000 

2.64575 

8.36660 

343.000 

1.91293 

4.12129 

8.87904 

.142857 

n 

n2 

V^ 

Vio  ?i 

n3 

3/  — 

\n 

^10"^ 

?100^ 

1/n 

106 


Powers  —  Roots  —  Reciprocals 


[VI 


n 

n2 

V^ 

VIoTi 

n3 

3l  

Vn 

^10  n 

\TOO~n 

l/n 

7.00 

49.0000 

2.64575 

8.36660 

343.000 

1.91293 

4.12129 

8.87904 

.142857 

7.01 
7.02 
7.03 

49.1401 
49.2804 
49.4209 

2.64764 
2.64953 
2.65141 

8.37257 
8.37854 
8.38451 

344.472 
345.948 
347.429 

1.91384 
1.91475 
1.91566 

4.12325 
4.12521 
4.12716 

8.88327 
8.88749 
8.89171 

.142653 
.142450 
.142248 

7.04 
7.05 
7.06 

49.5616 
49.7025 
49.8436 

2.65330 
2.65518 
2.65707 

8.39047 
8.39643 
8.40238 

348.914 
350.403 
351.896 

1.91657 
1.91747 
1.91838 

4.12912 
4.13107 
4.13303 

8.89592 
8.90013 
8.90434 

.142045 
.141844 
.141643 

7.07 
7.08 
7.09 

49.9849 
50.1264 
50.2681 

2.65895 
2.66083 
2.66271 

8.40833 
8.41427 
8.42021 

353.393 
354.895 
356.401 

1.91929 
1.92019 
1.92109 

4.13498 
4.13693 
4.13887 

8.90854 
8.91274 
8.91693 

.141443 
.141243 
.141044 

7.10 

50.4100 

2.66458 

8.42615 

357.911 

1.92200 

4.14082 

8.92112 

.140845 

7.11 
7.12 
7.13 

50.5521 
50.6944 
50.8369 

2.66646 
2.66833 
2.67021 

8.43208 
8.43801 
8.44393 

359.425 
360.944 
362.467 

1.92290 
1.92380 
1.92470 

4.14276 
4.14470 
4.14664 

8.92531 
8.92949 
8.93367 

.140647 
.140449 
.140252 

7.14 
7.15 
7.16 

50.9796 
51.1225 
51.2656 

2.67208 
2.67395 
2.67582 

8.44985 
8.45577 
8.46168 

363.994 
365.526 
367.062 

1.92560 
1.92650 
1.92740 

4.14858 
4.15052 
4.15245 

8.93784 
8.94201 
8.94618 

.140056 
.139860 
.139665 

7.17 
7.18 
7.19 

51.4089 
51.5524 
51.6961 

2.67769 
2.67955 
2.68142 

8.46759 
8.47349 
8.47939 

368.602 
370.146 
371.695 

1.92829 
1.92919 
1.93008 

4.15438 
4.15631 
4.15824 

8.95034 
8.95450 
8.95866 

.139470 
.139276 
.139082 

720 

51.8400 

2.68328 

8.48528 

373.248 

1.93098 

4.16017 

8.96281 

.138889 

7.21 
7.22 
7.23 

51.9841 
52.1284 
52.2729 

2.68514 
2.68701 
2.68887 

8.49117 
8.49706 
8.50294 

374.805 
376.367 
377.933 

1.93187 
1.93277 
1.93366 

4.16209 
4.16402 
4.16594 

8.96696 
8.97110 
8.97524 

.138696 
.138504 
.138313 

7.24 
7.25 
7.26 

52.4176 
52.5625 
52.7076 

2.69072 
2.69258 
2.69444 

8.50882 
8.51469 
8.52056 

379.503 
381.078 
382.657 

1.93455 
1.93544 
1.93633 

4.16786 
4.16978 
4.17169 

8.97938 
8.98351 
8.98764 

.138122 
.137931 
.137741 

7.27 

7.28 
7.29 

52.8529 
£2.9984 
53.1441 

2.69629 
2.69815 
2.70000 

8.52643 
8.53229 
8.53815 

384.241 
385.828 
387.420 

1.93722 
1.93810 
1.93899 

4.17361 
4.17552 
4.17743 

8.99176 
8.99588 
9.00000 

.137552 
.137363 
.137174 

7.30 

53.2900 

2.70185 

8.54400 

389.017 

1.93988 

4.17934 

9.00411 

.136986 

7.31 
7.32 
7.33 

53.4361 
53.5824 
53.7289 

2.70370 
2.70555 
2.70740 

8.54985 
8.55570 
8.56154 

390.618 
392.223 
393.833 

1.94076 
1.94165 
1.94253 

4.18125 
4.18315 
4.18506 

9.00822 
9.01233 
9.01643 

.136799 
.136612 
.136426 

7.34 
7.35 
7.36 

53.8756 
54.0225 
54.1696 

2.70924 
2.71109 
2.71293 

8.56738 
8.57321 
8.57904 

395.447 
397.065 
398.688 

1.94341 
1.94430 
1.94518 

4.18696 
4.18886 
4.19076 

9.02053 
9.02462 
9.02871 

.136240 
.136054 
.135870 

7.37 
7.38 
7.39 

54.3169 
54.4644 
54.6121 

2.71477 
2.71662 
2.71846 

8.58487 
8.59069 
8.59651 

400.316 
401.947 
403.583 

1.94606 
1.94694 
1.94782 

4.19266 
4.19455 
4.19644 

9.03280 
9.03689 
9.04097 

.135685 
.135501 
.135318 

7.40 

54.7600 

2.72029 

8.60233 

405.224 

1.94870 

4.19834 

9.04504 

.135135 

7.41 
7.42 
7.43 

54.9081 
55.0564 
55.2049 

2.72213 
2.72397 
2.72580 

8.60814 
8.61394 
8.61974 

406.869 
408.518 
410.172 

1.94957 
1.95045 
1.95132 

4.20023 
4.20212 
4.20400 

9.04911 
9.05318 
9.05725 

.134953 
.134771 
.134590 

7.44 
7.45 
7.46 

55.3536 
55.5025 
55.6516 

2.72764 
2.72947 
2.73130 

8.62554 
8.63134 
8.63713 

411.831 
413.494 
415.161 

1.95220 
1.95307 
1.95395 

4.20589 
4.20777 
4.20965 

9.06131 
9.06537 
9.06942 

.134409 
.134228 
.134048 

7.47 
7.48 
7.49 

55.8009 
55.9504 
56.1001 

2.73313 
2.73496 
2.73679 

8.64292 
8.64870 
8.65448 

416.833 
418.509 
420.190 

1.95482 
1.95569 
1.95656 

4.21153 
4.21341 
4.21529 

9.07347 
9.07752 
9.08156 

.133869 
.133690 
.133511 

7.50 

56.2500 

2.73861 

8.66025 

421.875 

1.95743 

4.21716 

9.08560 

.133333 

n 

n2 

V^ 

Vio/i 

n3 

^ 

3Wn 

?Ioo7i 

l/n 

VI] 


Powers  —  Roots  —  Reciprocals 


107 


n 

n2 

^ 

VlOn 

n3 

31  

Vn 

\/10  n 

\100  71 

l/n 

7.50 

56.2500 

2.73861 

8.66025 

421.875 

1.95743 

4.21716 

9.08560 

.133333 

7.51 
7.52 
7.53 

56.4001 
56.5504 
56.7009 

2.74044 
2.74226 
2.74408 

8.66603 
8.67179 
8.67756 

423.565 
425.259 
426.958 

1.95830 
1.95917 
1.96004 

4.21904 
4.22091 
4.22278 

9.08964 
9.09367 
9.09770 

.133156 
.132979 
.132802 

7.54 
7.55 
7.56 

56.8516 
57.0025 
57.1536 

2.74591 
2.74773 
2.74955 

8.68332 
8.68907 
8.69483 

428.661 
430.369 
432.081 

1.96091 
1.96177 
1.96264 

4.22465 
4.22651 
4.22838 

9.10173 
9.10575 
9.10977 

.132626 
.132450 
.132275 

7.57 
7.58 
7.59 

57.3049 
57.4564 
57.6081 

2.75136 
2.75318 
2.75500 

8.70057 
8.70632 
8.71206 

433.798 
435.520 
437.245 

1.96350 
1.96437 
1.96523 

4.23024 
4.23210 
4.23396 

9.11378 
9.11779 
9.12180 

.132100 
.131926 
.131752 

7.60 

57.7600 

2.75681 

8.71780 

438.976 

1.96610 

4.23582 

9.12581 

.131579 

7.61 
7.62 
7.63 

57.9121 
58.0644 
58.2169 

2.75862 
2.76043 
2.76225 

8.72353 
8.72926 
8.73499 

440.711 
442.451 
444.195 

1.96696 
1.96782 
1.96868 

4.23768 
4.23954 
4.24139 

9.12981 
9.13380 
9.13780 

.131406 
.131234 
.131062 

7.64 
7.65 
7.66 

58.3696 
58.5225 
58.6756 

2.76405 
2.76586 
2.76767 

8.74071 
8.74643 
8.75214 

445.944 
447.697 
449.455 

1.96954 
1.97040 
1.97126 

4.24324 
4.24509 
4.24694 

9.14179 
9.14577 
9.14976 

.130890 
.130719 
.130548 

7.67 
7.68 
7.69 

58.8289 
58.9824 
59.1361 

2.76948 
2.77128 
2.77308 

8.75785 
8.76356 
8.76926 

451.218 
452.985 
454.757 

1.97211 
1.97297 
1.97383 

4.24879 
4.25063 
4.25248 

9.15274 
9.15771 
9.16169 

.130378 
.130208 
.130039 

7.70 

59.2900 

2.77489 

8.77496 

456.533 

1.97468 

4.25432 

9.16566 

.129870 

7.71 
V.72 
7.73 

59.4441 
59.5984 
59.7529 

2.77669 
2.77849 
2.78029 

8.78066 
8.78635 
8.79204 

458.314 
460.100 
461.890 

1.97554 
1.97639 
1.97724 

4.25616 
4.25800 
4.25984 

9.16962 
9.17359 
9.17754 

.129702 
.129534 
.129366 

7.74 
7.75 
7.76 

59.9076 
60.0625 
60.2176 

2.78209 
2.78388 
2.78568 

8.79773 
8.80341 
8.80909 

463.685 
465.484 
467.289 

1.97809 
1.97895 
1.97980 

4.26167 
4.26351 
4.26534 

9.18150 
9.18545 
9.18940 

.129199 
.129032 
.128866 

7.77 
7.78 
7.79 

60.3729 
60.5284 
60.6841 

2.78747 
2.78927 
2.79106 

8.81476 
8.82043 
8.82610 

469.097 
470.911 

472.729 

1.98065 
1.98150 
1.98234 

4.26717 
4.26900 
4.27083 

9.19335 
9.19729 
9.20123 

.128700 
.128535 
.128370 

7.80 

60.8400 

2.79285 

8.83176 

474.552 

1.98319 

4.27266 

9.20516 

.128205 

7.81 
7.82 
7.83 

60.9961 
61.1524 
61.3089 

2.79464 
2.79643 
2.79821 

8.83742 
8.84308 
8.84873 

476.380 
478.212 
480.049 

1.98404 
1.98489 
1.98573 

4.27448 
4.27631 
4.27813 

9.20910 
9.21302 
9.21695 

.128041 
.127877 
.127714 

7.84 
7.85 
7.86 

61.4656 
61.6225 
61.7796 

2.80000 
2.80179 
2.80357 

8.85438 
8.86002 
8.86566 

481.890 
483.737 
485.588 

1.98658 
1.98742 
1.98826 

4.27995 
4.28177 
4.28359 

9.22087 
9.22479 
9.22871 

.127551 
.127389 
.127226 

7.87 
7.88 
7.89 

61.9369 
62.0944 
62.2521 

2.80535 
2.80713 
2.80891 

8.87130 
8.87694 

8.88257 

487.443 
489.304 
491.169 

1.98911 
1.98995 
1.99079 

4.28540 
4.28722 
4.28903 

9.23262 
9.23653 
9.24043 

.127065 
.126904 
.126743 

7.90 

62.4100 

2.81069 

8.88819 

493.039 

1.99163 

4.29084 

9.24434 

.126582 

7.91 
7.92 
7.93 

62.5681 
62.7264 
62.8849 

2.81247 
2.81425 
2.81603 

8.89382 
8.89944 
8.90505 

494.914 
496.793 
498.677 

1.99247 
1.99331 
1.99415 

4.29265 
4.29446 
4.29627 

9.24823 
9.25213 
9.25602 

.126422 
.126263 
.126103 

7.94 
7.95 
7.96 

63.0436 
63.2025 
63.3616 

2.81780 
2.81957 
2.82135 

8.91067 
8.91628 
8.92188 

500.566 
502.460 
504.358 

1.99499 
1.99582 
1.99666 

4.29807 
4.29987 
4.30168 

9.25991 
9.26380 
9.26768 

.125945 
.125786 
.125628 

7.97 
7.98 
7.99 

63.5209 
63.6804 
63.8401 

2.82312 
2.82489 
2.82666 

8.92749 
8.93308 
8.93868 

506.262 
508.170 
510.082 

1.99750 
1.99833 
1.99917 

4.30348 
4.30528 
4.30707 

9.27156 
9.27544 
9.27931 

.125471 
.125313 
.125156 

8.00 

64.0000 

2.82843 

8.94427 

512.000 

2.00000 

4.30887 

9.28318 

.125000 

n, 

n~ 

Vn 

^^l(^^ 

n3 

£» 

IWTi 

^TooTT 

l/n 

108 


Powers  —  Roots  —  Reciprocals 


[VI 


n 

n2 

V^ 

VlOn 

n3 

31  

S/n, 

^10  n 

\^100n 

l/n 

8.00 

64.0000 

2.82843 

8.94427 

512.000 

2.00000 

4.30887 

9.28318 

.125000 

8.01 
8.02 
8.03 

64.1601 
64.3204 
64.4809 

2.83019 
2.83196 
2.83373 

8.94986 
8.95545 
8.96103 

513.922 
515.850 
517.782 

2.00083 
2.00167 
2.00250 

4.31066 
4.31246 
4.31425 

9.28704 
9.29091 
9.29477 

.124844 
.124688 
.124533 

8.04 
8.05 
8.06 

64.6416 
64.8025 
64.9636 

2.83549 
2.83725 
2.83901 

8.96660 
8.97218 
8.97775 

519.718 
521.660 
523.607 

2.00333 
2.00416 
2.00499 

4.31604 
4.31783 
4.31961 

9.29862 
9.30248 
9.30633 

.124378 
.124224 
.124069 

8.07 
8.08 
8.09 

65.1249 
65.2864 
65.4481 

2.84077 
2.84253 
2.84429 

8.98332 
8.98888 
8.99444 

525.558 
527.514 
529.475 

2.00582 
2.00664 
2.00747 

4.32140 
4.32318 
4.32497 

9.31018 
9.31402 
9.31786 

.123916 
.123762 
.123609 

8.10 

65.6100 

2.84605 

9.00000 

531.441 

2.00830 

4.32675 

9.32170 

.123457 

8.11 
8.12 
8.13 

65.7721 
65.9344 
66.0969 

2.84781 
2.84956 
2.85132 

9.00555 
9.01110 
9.01665 

533.412 
535.387 
537.368 

2.00912 
2.00995 
2.01078 

4.32853 
4.33031 
4.33208 

9.32553 
9.32936 
9.33319 

.123305 
.123153 
.123001 

8.14 
8.15 
8.16 

66.2596 
66.4225 
66.5856 

2.85307 
2.85482 
2.85657 

9.02219 
9.02774 
9.03327 

539.353 
541.343 
543.338 

2.01160 
2.01242 
2.01325 

4.33386 
4.33563 
4.33741 

9.33702 
9.34084 
9.34466 

.122850 
.122699 
.122549 

8.17 
8.18 
8.19 

66.7489 
66.9124 
67.0761 

2.85832 
2.86007 
2.86182 

9.03881 
9.04434 
9.04986 

545.339 
547.343 
549.353 

2.01407 
2.01489 
2.01571 

4.33918 
4.34095 
4.34271 

9.34847 
9.35229 
9.35610 

.122399 
.122249 
.122100 

8J20 

67.2400 

2.86356 

9.05539 

551.368 

2.01653 

4.34448 

9.35990 

.121951 

8.21 
8.22 
8.23 

67.4041 
67.5684 
67.7329 

2.86531 
2.86705 
2.86880 

9.06091 
9.06642 
9.07193 

553.388 
555.412 
557.442 

2.01735 
2.01817 
2.01899 

4.34625 
4.34801 
4.34977 

9.36370 
9.36751 
9.37130 

.121803 
.121655 
.121507 

8.24 
8.25 
8.26 

67.8976 
68.0625 
68.2276 

2.87054 
2.87228 
2.87402 

9.07744 
9.08295 
9.08845 

559.476 
561.516 
563.560 

2.01980 
2.02062 
2.02144 

4.35153 
4.35329 
4.35505 

9.37510 
9.37889 
9.38268 

.121359 
.121212 
.121065 

8.27 
8.28 
8.29 

68.3929 
68.5584 
68.7241 

2.87576 
2.87750 

2.87924 

9.09395 
9.09945 
9.10494 

565.609 
567.664 
569.723 

2.02225 
2.02307 
2.02388 

4.35681 
4.35856 
4.36032 

9.38646 
9.39024 
9.39402 

.120919 
.120773 
.120627 

8.30 

68.8900 

2.88097 

9.11043 

571.787 

2.02469 

4.36207 

9.39780 

.120482 

8.31 
8.32 
8.33 

69.0561 
69.2224 
69.3889 

2.88271 
2.88444 
2.88617 

9.11592 
9.12140 
9.12688 

573.856 
575.930 
578.010 

2.02551 
2.02632 
2.02713 

4.36382 
4.36557 
4.36732 

9.40157 
9.40534 
9.40911 

.120337 
.120192 
.120048 

8.34 
8.35 
8.36 

69.5556 
69.7225 
69.8896 

2.88791 
2.88964 
2.89137 

9.13236 
9.13783 
9.14330 

580.094 
582.183 
584.277 

2.02794 
2.02875 
2.02956 

4.36907 
4.37081 
4.37256 

9.41287 
9.41663 
9.42039 

.119904 
.119760 
.119617 

8.37 
8.38 
8.39 

70.0569 

70.2244 
70.3921 

2.89310 

2.89482 
2.89655 

9.14877 
9.15423 
9.15969 

586.376 
588.480 
590.590 

2.03037 
2.03118 
2.03199 

4.37430 
4.37604 

4.37778 

9.42414 
9.42789 
9.43164 

.119474 
.119332 
.119190 

8.40 

70.5600 

2.89828 

9.16515 

592.704 

2.03279 

4.37952 

9.43539 

.119048 

8.41 
8.42 
8.43 

70.7281 
70.8964 
71.0649 

2.90000 
2.90172 
2.90345 

9.17061 
9.17606 
9.18150 

594.823 
596.948 
599.077 

2.03360 
2.03440 
2.03521 

4.38126 
4.38299 
4.38473 

9.43913 
9.44287 
9.44661 

.118906 
.118765 
.118624 

8.44 
8.45 
8.46 

71.2336 
71.4025 
71.5716 

2.90517 
2.90689 
2.90861 

9.18695 
9.19239 
9.19783 

601.212 
603.351 
605.496 

2.03601 
2.03682 
2.03762 

4.38646 
4.38819 
4.38992 

9.45034 
9.45407 
9.45780 

.118483 
.118343 
.118203 

8.47 
8.48 
8.49 

71.7409 
71.9104 
72.0801 

2.91033 
2.91204 
2.91376 

9.20326 
9.20869 
9.21412 

607.645 
609.800 
611.960 

2.03842 
2.03923 
2.04003 

4.39165 
4.39338 
4.39510 

9.46152 
9.46525 
9.46897 

.118064 
.117925 

.117786 

8.50 

72.2500 

2.91548 

9.21954 

614.125 

2.04083 

4.39683 

9.47268 

.117647 

n 

n2 

V^ 

VlO  n 

n3 

31  — 

\n 

\loH 

^lOOn 

l/n 

VI] 


Powers  —  Roots  —  Reciprocals 


109 


n 

n2 

^ 

\lo^ 

n3 

££ 

^10  n 

^100  n 

l/n 

8.50 

72.2500 

2.91548 

9.21954 

614.125 

2.04083 

4.39683 

9.47268 

.117647 

8.51 
8.52 
8.53 

72.4201 
72.5904 
72.7609 

2.91719 
2.91890 
2.92062 

9.22497 
9.23038 
9.23580 

616.295 
618.470 
620.650 

2.04163 
2.04243 
2.04323 

4.39855 
4.40028 
4.40200 

9.47640 
9.48011 
9.48381 

.117509 
.117371 
.117233 

8.54 
8.55 
8.56 

72.9316 
73.1025 
73.2736 

2.92233 
2.92404 
2.92575 

9.24121 
9.24662 
9.25203 

622.836 
625.026 
627.222 

2.04402 
2.04482 
2.04562 

4.40372 
4.40543 
4.40715 

9.48752 
9.49122 
9.49492 

.117096 
.116959 
.116822 

8.57 

8.58 
8.59 

73.4449 
73.6164 

73.7881 

2.92746 
2.92916 
2.93087 

9.25743 
9.26283 
9.26823 

629.423 
631.629 
633.840 

2.04641 
2.04721 
2.04801 

4.40887 
4.41058 
4.41229 

9.49861 
9.50231 
9.50600 

.116686 
.116550 
.116414 

8.60 

73.9600 

2.9325S 

9.27362 

636.056 

2.04880 

4.41400 

9.50969 

.116279 

8.61 
8.62 
8.63 

74.1321 
74.3044 
74.4769 

2.93428 
2.93598 
2.93769 

9.27901 
9.28440 
9.28978 

638.277 
640.504 
642.736 

2.04959 
2.05039 
2.05118 

4.41571 
4.41742 
4.41913 

9.51337 
9.51705 
9.52073 

.116144 
.116009 
.115875 

8.64 
8.65 
8.66 

74.6496 
74.8225 
74.9956 

2.93939 
2.94109 
2.94279 

9.29516 
9.30054 
9.30591 

644.973 
647.215 
649.462 

2.05197 
2.05276 
2.05355 

4.42084 
4.42254 
4.42425 

9.52441 
9.52808 
9.53175 

.115741 
.115607 
.115473 

8.67 
8.68 
8.69 

75.1689 
75.3424 
75.5161 

2.94449 
2.94618 
2.94788 

9.31128 
9.31665 
9.32202 

651.714 
653.972 
656.235 

2.05434 
2.05513 

2.05592 

4.42595 
4.42765 
4.42935 

9.53542 
9.53908 
9.54274 

.115340 
.115207 
.115075 

8.70 

75.6900 

2.94958 

9.32738 

658.503 

2.05671 

4.43105 

9.54640 

.114943 

8.71 
8.72 
8.73 

75.8641 
76.0384 
76.2129 

2.95127 
2.95296 
2.95466 

9.33274 
9.33809 
9.34345 

660.776 
663.055 
665.339 

2.05750 
2.05828 
2.05907 

4.43274 
4.43444 
4.43613 

9.55006 
9.55371 
9.55736 

.114811 
.114679 
.114548 

8.74 
8.75 
8.76 

76.3876 
76.5625 
76.7376 

2.95635 
2.95804 
2.95973 

9.34880 
9.35414 
9.35949 

667.628 
669.922 
672.221 

2.05986 
2.06064 
2.06143 

4.43783 
4.43952 
4.44121 

9.56101 
9.56466 
9.56830 

.114416 
.114286 
.114155 

8.77 
8.78 
8.79 

76.9129 
77.0884 
77.2641 

2.96142 
2.96311 
2.96479 

9.36483 
9.37017 
9.37550 

674.526 
676.836 
679.151 

2.06221 
2.06299 
2.06378 

4.44290 
4.44459 
4.44627 

9.57194 
9.57557 
9.57921 

.114025 
.113895 
.113766 

8.80 

77.4400 

2.96648 

9.38083 

681.472 

2.06456 

4.44796 

9.58284 

.113636 

8.81 
8.82 
8.83 

77.6161 

77.7924 
77.9689 

2.96816 
2.96985 
2.97153 

9.38616 
9.39149 
9.39681 

683.798 
686.129 
688.465 

2.06534 
2.06612 
2.06690 

4.44964 
4.45133 
4.45301 

9.58647 
9.59009 
9.59372 

.113507 
.113379 
.113250 

8.84 
8.85 
8.86 

78.1456 
78.3225 
78.4996 

2.97321 

2.97489 
2.97658 

9.40213 
9.40744 
9.41276 

690.807 
693.154 
695.506 

2.06768 
2.06846 
2.06924 

4.45469 
4.45637 
4.45805 

9.59734 
9.60095 
9.60457 

.113122 
.112994 
.112867 

8.87 
8.88 
8.89 

78.6769 
78.8544 
79.0321 

2.97825 
2.97993 
2.98161 

9.41807 
9.42338 
9.42868 

697.864 
700.227 
702.595 

2.07002 
2.07080 
2.07157 

4.45972 
4.46140 
4.46307 

9.60818 
9.61179 
9.61540 

.112740 
.112613 

.112486 

8.90 

79.2100 

2.98329 

9.43398 

704.969 

2.07235 

4.46475 

9.61900 

.112360 

8.91 
8.92 
8.93 

79.3881 
79.5664 
79.7449 

2.98496 
2.98664 
2.98831 

9.43928 
9.44458 
9.44987 

707.348 
709.732 

712.122 

2.07313 
2.07390 
2.07468 

4.46642 
4.46809 
4.46976 

9.62260 
9.62620 
9.62980 

.112233 
.112108 
.111982 

8.94 
8.95 
8.96 

79.9236 
80.1025 
80.2816 

2.98998 
2.99166 
2.99333 

9.45516 
9.46044 
9.46573 

714.517 
716.917 
719.323 

2.07545 
2.07622 
2.07700 

4.47142 
4.47309 

4.47476 

9.63339 
9.63698 
9.64057 

.111857 
.111732 
.111607 

8.97 
8.98 
8.99 

80.4609 
80.6404 
80.8201 

2.99500 
2.99666 
2.99833 

9.47101 
9.47629 
9.48156 

721.734 
724.151 
726.573 

2.07777 
2.07854 
2.07931 

4.47642 
4.47808 
4.47974 

9.64415 
9.64774 
9.65132 

.111483 
.111359 
.111235 

9.00 

81.0000 

3.00000 

9.48683 

729.000 

2.08008 

4.48140 

9.65489 

.111111 

n 

n2 

V^ 

VlOre 

n3 

^ 

\To~^ 

^100^ 

l/n 

110 


Powers  —  Roots  —  Reciprocals 


[VI 


n 

n2 

V7T 

VIoTI 

n3 

3/  — 
\n 

W^ 

I/mm 

l/n 

9.00 

81.0000 

3.00000 

9.48683 

729.000 

2.08008 

4.48140 

9.65489 

.111111 

9.01 
9.02 
9.03 

81.1801 
81.3604 
81.5409 

3.00167 
3.00333 
3.00500 

9.49210 
9.49737 
9.50263 

731.433 
733.871 
736.314 

2.08085 
2.08162 
2.08239 

4.48306 
4.48472 
4.48638 

9.65847 
9.66204 
9.66561 

.110988 
.110865 
.110742 

9.04 
9.05 
9.06 

81.7216 
81.9025 
82.0836 

3.00666 
3.00832 
3.00998 

9.50789 
9.51315 
9.51840 

738.763 

741.218 
743.677 

2.08316 
2.08393 
2.08470 

4.48803 
4.48969 
4.49134 

9.66918 
9.67274 
9.67630 

.110619 
.110497 
.110375 

9.07 
9.08 
9.09 

82.2649 
82.4464 
82.6281 

3.01164 
3.01330 
3.01496 

9.52365 
9.52890 
9.53415 

746.143 
748.613 
751.089 

2.08546 
2.08623 
2.08699 

4.49299 
4.49464 
4.49629 

9.67986 
9.68342 
9.68697 

.110254 
.110132 
.110011 

9.10 

82.8100 

3.01662 

9.53939 

753.571 

2.08776 

4.49794 

9.69052 

.109890 

9.11 
9.12 
9.13 

82.9921 
83.1744 
83.3569 

3.01828 
3.01993 
3.02159 

9.54463 
9.54987 
9.55510 

756.058 
758.551 
761.048 

2.08852 
2.08929 
2.09005 

4.49959 
4.50123 
4.50288 

9.69407 
9.69762 
9.70116 

.109769 
.109649 
.109529 

9.14 
9.15 
9.16 

83.5396 
83.7225 
83.9056 

3.02324 
3.02490 
3.02655 

9.56033 
9.56556 
9.57079 

763.552 
766.061 

768.575 

2.09081 
2.09158 
2.09234 

4.50452 
4.50616 
4.50781 

9.70470 
9.70824 
9.71177 

.109409 
.109290 
.109170 

9.17 
9.18 
9.19 

84.0889 
84.2724 
84.4561 

3.02820 
3.02985 
3.03150 

9.57601 
9.58123 
9.58645 

771.095 
773.621 
776.152 

2.09310 
2.09386 
2.09462 

4.50945 
4.51108 
4.51272 

9.71531 

9.71884 
9.72236 

.109051 
.108932 
.108814 

9.20 

84.6400 

3.03315 

9.59166 

778.688 

2.09538 

4.51436 

9.72589 

.108696 

9.21 
9.22 
9.23 

84.8241 
85.0084 
85.1929 

3.03480 
3.03645 
3.03809 

9.59687 
9.60208 
9.60729 

781.230 
783.777 
786.330 

2.09614 
2.09690 
2.09765 

4.51599 
4.51763 
4.51926 

9.72941 
9.73293 
9.73645 

.108578 
.108460 
.108342 

9.24 
9.25 
9.26 

85.3776 
85.5625 
85.7476 

3.03974 
3.04138 
3.04302 

9.61249 
9.61769 
9.62289 

788.889 
791.453 
794.023 

2.09841 
2.09917 
2.09992 

4.52089 
4.52252 
4.52415 

9.73996 

9.74348 
9.74699 

.108225 
.108108 
.107991 

9.27 
9.28 
9.29 

85.9329 

86.1184 
86.3041 

3.04467 
3.04631 
3.04795 

9.62808 
9.63328 
9.63846 

796.598 
799.179 
801.765 

2.10068 
2.10144 
2.10219 

4.52578 
4.52740 
4.52903 

9.75049 
9.75400 
9.75750 

.107875 
.107759 
.107643 

9.30 

86.4900 

3.04959 

9.64365 

804.357 

2.10294 

4.53065 

9.76100 

.107527 

9.31 
9.32 
9.33 

86.6761 
86.8624 
87.0489 

3.05123 
3.05287 
3.05450 

9.64883 
9.65401 
9.65919 

806.954 
809.558 
812.166 

2.10370 
2.10445 
2.10520 

4.53228 
4.53390 
4.53552 

3.76450 
9.76799 
9.77148 

.107411 
.107296 
.107181 

9.34 
9.35 
9.36 

87.2356 
87.4225 
87.6096 

3.05614 
3.05778 
3.05941 

9.66437 
9.66954 
9.67471 

814.781 
817.400 
820.026 

2.10595 
2.10671 
2.10746 

4.53714 
4.53876 
4.54038 

9.77497 
9.77846 
9.78195 

.107066 
.106952 
.106838 

9.37 
9.38 
9.39 

87.7969 
87.9844 
88.1721 

3.06105 
3.06268 
3.06431 

9.67988 
9.68504 
9.69020 

822.657 
825.294 
827.936 

2.10821 
2.10896 
2.10971 

4.54199 
4.54361 

4.54522 

9.78543 
9.78891 
9.79239 

.106724 
.106610 
.106496 

9.40 

88.3600 

3.06594 

9.69536 

830.584 

2.11045 

4.54684 

9.79586 

.106383 

9.41 
9.42 
9.43 

88.5481 
88.7364 
88.9249 

3.06757 
3.06920 
3.07083 

9.70052 
9.70567 
9.71082 

833.238 
835.897 
838.562 

2.11120 
2.11195 
2.11270 

4.54845 
4.55006 
4.55167 

9.79933 
9.80280 
9.80627 

.106270 
.106157 
.106045 

9.44 
9.45 
9.46 

89.1136 
89.3025 
89.4916 

3.07246 
3.07409 
3.07571 

9.71597 
9.72111 
9.72625 

841.232 
843.909 
846.591 

2.11344 
2.11419 
2.11494 

4.55328 
4.55488 
4.55649 

9.80974 
9.81320 
9.81666 

.105932 
.105820 
.105708 

9.47 
9.48 
9.49 

89.6809 
89.8704 
90.0601 

3.07734 
3.07896 
3.08058 

9.73139 
9.73653 
9.74166 

849.278 
851.971 
854.670 

2.11568 
2.11642 
2.11717 

4.55809 
4.55970 
4.56130 

9.82012 
9.82357 
9.82703 

.105597 
.105485 
.105374 

9.50 

90.2500 

3.08221 

9.74679 

857.375 

2.11791 

4.56290 

9.83048 

.105263 

n 

n2 

V^ 

VlOn 

n3 

3I  — 
\n 

JfWn 

^TooTi 

l/n 

Powers  —  Roots  —  Reciprocals 


111 


n 

n2 

V^ 

VToTi 

n3 

3/  — 

Vn 

-\fW7i 

^looH 

l/n 

9.50 

90.2500 

3.08221 

9.74679 

857.375 

2.11791 

4.56290 

9.83048 

.105263 

9.51 
9.52 
9.53 

90.4401 
90.6304 
90.8209 

3.08383 
3.08545 
3.08707 

9.75192 
9.75705 
9.76217 

860.085 
862.801 
865.523 

2.11865 
2.11940 
2.12014 

4.56450 
4.56610 
4.56770 

9.83392 
9.83737 
9.84081 

.105152 
.105042 
.104932 

9.54 
9.55 
9.56 

91.0116 
91.2025 
91.3936 

3.08869 
3.09031 
3.09192 

9.76729 
9.77241 
9.77753 

868.251 
870.984 
873.723 

2.12088 
2.12162 
2.12236 

4.56930 
4.57089 
4.57249 

9.84425 
9.84769 
9.85113 

.104822 
.104712 
.104603 

9.57 
9.58 
9.59 

91.5849 
91.7764 
91.9681 

3.09354 
3.09516 
3.09677 

9.78264 
9.78775 
9.79285 

876.467 
879.218 
881.974 

2.12310 
2.12384 
2.12458 

4.57408 
4.57567 
4.57727 

9.85456 
9.85799 
9.86142 

.104493 
.104384 
.104275 

9.60 

92.1600 

3.09839 

9.79796 

884.736 

2.12532 

4.57886 

9.86485 

.104167 

9.61 
9.62 
9.63 

92.3521 
92.5444 
92.7369 

3.10000 
3.10161 
3.10322 

9.80306 
9.80816 
9.81326 

887.504 
890.277 
893.056 

2.12605 
2.12679 
2.12753 

4.58045 
4.58204 
4.58362 

9.86827 
9.87169 
9.87511 

.104058 
.103950 
.103842 

9.64 
9.65 
9.66 

92.9296 
93.1225 
93.3156 

3.10483 
3.10644 
3.10805 

9.81835 
9.82344 
9.82853 

895.841 
898.632 
901.429 

2.12826 
2.12900 
2.12974 

4.58521 
4.58679 
4.58838 

9.87853 
9.88195 
9.88536 

.103734 
.103627 
.103520 

9.67 
9.68 
9.69 

93.5089 
93.7024 
93.8961 

3.10966 
3.11127 
3.11288 

9.83362 
9.83870 
9.84378 

904.231 
907.039 
909.853 

2.13047 
2.13120 
2.13194 

4.58996 
4.59154 
4.59312 

9.88877 
9.89217 
9.89558 

.103413 
.103306 
.103199 

9.70 

94.0900 

3.11448 

9.84886 

912.673 

2.13267 

4.59470 

9.89898 

.103093 

9.71 
9.72 
9.73 

94.2841 
94.4784 
94.6729 

3.11609 
3.11769 
3.11929 

9.85393 
9.85901 
9.86408 

915.499 
918.330 
921.167 

2.13340 
2.13414 
2.13487 

4.59628 
4.59786 
4.59943 

9.90238 
9.90578 
9.90918 

.102987 
.102881 
.102775 

9.74 
9.75 
9.76 

94.8676 
95.0625 
95.2576 

3.12090 
3.12250 
3.12410 

9.86914 
9.87421 
9.87927 

924.010 
926.859 
929.714 

2.13560 
2.13633 
2.13706 

4.60101 
4.60258 
4.60416 

9.91257 
9.91596 
9.91935 

.102669 
.102564 
.102459 

9.77 

9.78 
9.79 

95.4529 
95.6484 
95.8441 

3.12570 
3.12730 
3.12890 

9.88433 
9.88939 
9.89444 

932.575 
935.441 
938.314 

2.13779 
2.13852 
2.13925 

4.60573 
4.60730 
4.60887 

9.92274 
9.92612 
9.92950 

.102354 
.102249 
.102145 

9.80 

96.0400 

3.13050 

9.89949 

941.192 

2.13997 

4.61044 

9.93288 

.102041 

9.81 
9.82 
9.83 

96.2361 
96.4324 
96.6289 

3.13209 
3.13369 
3.13528 

9.90454 
9.90959 
9.91464 

944.076 
946.966 
949.862 

2.14070 
2.14143 
2.14216 

4.61200 
4.61357 
4.61514 

9.93626 
9.93964 
9.94301 

.101937 
.101833 
.101729 

9.84 
9.85 
9.86 

96.8256 
97.0225 
97.2196 

3.13688 
3.13847 
3.14006 

9.91968 
9.92472 
9.92975 

952.764 
955.672 
958.585 

2.14288 
2.14361 
2.14433 

4.61670 
4.61826 
4.61983 

9.94638 
9.94975 
9.95311 

.101626 
.101523 
.101420 

9.87 
9.88 
9.89 

97.4169 
97.6144 
97.8121 

3.14166 
3.14325 

3.14484 

9.93479 
9.93982 
9.94485 

961.505 
964.430 
967.362 

2.14506 
2.14578 
2.14651 

4.62139 
4.62295 
4.62451 

9.95648 
9.95984 
9.96320 

.101317 
.101215 
.101112 

9.90 

98.0100 

3.14643 

9.94987 

970.299 

2.14723 

4.62607 

9.96655 

.101010 

9.91 
9.92 
9.93 

98.2081 
98.4064 
98.6049 

3.14802 
3.14960 
3.15119 

9.95490 
9.95992 
9.96494 

973.242 
976.191 
979.147 

2.14795 
2.14867 
2.14940 

4.62762 
4.62918 
4.63073 

9.96991 
9.97326 
9.97661 

.100908 
.100806 
.100705 

9.94 
9.95 
9.96 

98.8036 
99.0025 
99.2016 

3.15278 
3.15436 
3.15595 

9.96995 
9.97497 
9.97998 

982.108 
985.075 
988.048 

2.15012 
2.15084 
2.15156 

4.63229 
4.63384 
4.63539 

9.97996 
9.98331 
9.98665 

.100604 
.100503 
.100402 

9.97 
9.98 
9.99 

99.4009 
99.6004 
99.8001 

3.15753 
3.15911 
3.16070 

9.98499 
9.98999 
9.99500 

991.027 
994.012 
997.003 

2.15228 
2.15300 
2.15372 

4.63694 
4.63849 
4.64004 

9.98999 
9.99333 
9.99667 

.100301 
.100200 
.100100 

10.00 

100.000 

3.16228 

10.0000 

1000.00 

2.15443 

4.64159 

10.0000 

.100000 

n 

n2 

V^ 

VioH 

n3 

£jj 

\lo^ 

JITwTi 

l/n 

112          Table  VII  —  Napierian  or  Natural  Logarithms         [VII 


N 

0 

123 

456 

789 

0.0 

5.395  6.088  6.493 

6.781  7.004  7.187 

7.341  7.474  7.592 

0.1 
0.2 
0.3 

0.4 
0.5 
0.6 

0.7 
0.8 
0.9 

3    7.697 
I    8.391 
§   8.796 

1   9.084 
S    9.307 
]3  -9^89 

?    9.643 
-3    9.777 
*-    9.895 

7.793  7.880  7.960 
8.439  8.486  8.530 
8.829  8.861  8.891 

9.108  9.132  9.156 
9.327  9.346  9.365 
9.506  9.522  9.538 

9.658  9.671  9.685 
9.789  9.802  9.814 
9.906  9.917  9.927 

8.034  8.103  8.167 
8.573  8.614  8.653 
8.921  8.950  8.978 

9.179  9.201  9.223 
9.384  9.402  9.420 
9.554  9.569  9.584 

9.699  9.712  9.726 
9.826  9.837  9.849 
9.938  9.949  9.959 

8.228  8.285  8.339 
8.691  8.727  8.762 
9.006  9.032  9.058 

9.245  9.266  9.287 
9.438  9.455  9.472 
9.600  9.614  9.629 

9.739  9.752  9.764 
9.861  9.872  9.883 
9.970  9.980  9.990 

1.0 

0.00000 

0995    1980  (2956 

3922    4879    5827 

6706    7696    8618 

1.1 

1.2 
1.3 

1.4 
1.5 
1.6 

1.7 
1.8 
1.9 

9531 
0.1  8232 
0.2  6236 

0.3  3647 
0.4  0547 
7pOO 

0.5  3063 

8779 
0.64185 

*0436  *1333  *2222 
9002    9885*0701 
7003   7763    8518 

4359    5066    5767 
1211    1871    2527 
7623    8243    8858 

3649   4232   4812 
9333    9884*0432 
4710    5233    5752 

*3103  *3976  *4842 
*1511  *2314  *3111 
9267  *0010  *0748 

6464    7156   7844 
3178   3825   4469 
9470  *0078  *06820 

5389    5962    6531 
*0977  *1519  *2058 
6269    6783    7294 

*5700  *6551  *7395 
*3902  *4686  *5464 
*1481  *2208  *2930 

8526    9204    9878 
5108    5742    6373 
*1282  *1879  *2473 

7098    7661    8222 
*2594  *3127  *3658 
7803    8310    8813 

2.0 

9315 

9813  *0310  *0804 

*1295  *1784  *2271 

*2755  *3237  *3716 

2.1 
2.2 
2.3 

2.4 

2.5 
2.6 

2.7 

2.8 
2.9 

0.7  4194 
8846 
0.8  3291 

7547 
0.9  1629 
6551 

9325 
1.0  2962 
6471 

4669    5142    5612 
9299    9751  *0200 
3725   4157   4587 

7963    8377   8789 
2028    2426    2822 
6935   6317   6698 

9695  *0063  *0430 
3318   3674   4028 
6815    7158   7500 

6081    6547    7011 
*0648  *1093  *1536 
6015    5442    5866 

9200   9609*0016 
3216    3609    4001 
7078   7456   7833 

*0796  *1160  *1523 
4380   4732    5082 
7841    8181    8519 

7473    7932    8390 
*1978  *2418  *2855 
6289    6710    7129 

*0422  *0826  *1228 
4391    4779    5166 
8208    8582    8954 

*1885  *2245  *2604 
5431    5779    6126 
8856    9192    9527 

3.0 

9861 

*0194  *0526  *0856 

*1186  *1514  *1841 

*2168  *2493  *2817 

3.1 
3.2 
3.3 

3.4 
3.5 
3.6 

3.7 
3.8 
3.9 

1.1  3140 
6315 
9392 

1.2  2378 
5276 
8093 

1.3  0833 
3500 
6098 

3462    3783    4103 
6627    6938    7248 
9695    9996*0297 

2671    2964   3256 
5562    5846    6130 
8371    8647   8923 

1103    1372    1641 
3763    4025   4286 
6354    6609    6864 

4422    4740    5057 
7557    7865   8173 
*0597  *0896  *1194 

3547    3837    4127 
6413    6695    6976 
9198   9473   9746 

1909   2176   2442 
4547    4807    5067 
7118   7372   7624 

5373    5688    6002 
8479    8784    9089 
*1491  *1788  *2083 

4415    4703    4990 
7257    7536    7815 
*0019  *0291  *0563 

2708    2972    3237 
5325    5584    5841 
7877    8128    8379 

4.0 

8629 

8879    9128    9377 

9624    9872*0118 

*0364  *0610  *0854 

4.1 
4.2 
4.3 

4.4 
4.5 
4.6 

4.7 
4.8 
4.9 

1.4  1099 
3508 
5862 

8160 
1.5  0408 
2606 

4756 
6862 
8924 

1342    1585    1828 
3746    3984    4220 
6094    6326    6557 

8387    8614    8840 
0630    0851    1072 
2823    3039    3256 

4969   5181    5393 
7070   7277   7485 
9127    9331    9534 

2070    2311    2552 
4456   4692    4927 
6787    7018   7247 

9065    9290   9515 
1293    1513    1732 
3471    3687    3902 

5604    5814   6025 
7691    7898    8104 
9737    9939*0141 

2792    3031    3270 
5161    5395    5629 
7476    7705    7933 

9739    9962  *0185 
1951    2170    2388 
4116    4330   4543 

6235    6444    6653 
8309    8515    8719 
*0342  *0543  *0744 

5.0 

1.6  0944 

1144    1343    1542 

1741    1939    2137 

2334    2531    2728 

N 

0 

123 

456 

789 

VII] 


Napierian  or  Natural  Logarithms 


N 

0 

123 

456 

789 

5.0 

1.6  0944 

1144  1343  1542 

1741  1939  2137 

2334  2531  2728 

5.1 
5.2 
5.3 

2924 
4866 
6771 

3120  3315  3511 
5058  5250  5441 
6959  7147  7335 

3705  3900  4094 
6632  5823  6013 
7523  7710  7896 

4287  4481  4673 
6203  6393  6582 
8083  8269  8455 

5.4 
5.5 
5.6 

8640 
1.7  0475 
2277 

8825  9010  9194 
0656  0838  1019 
2455  2633  2811 

9378  9562  9745 
1199  1380  1560 
2988  3166  3342 

9928  *0111  *0293 
1740  1919  2098 
3519  3695  3871 

5.7 
5.8 
5.9 

4047 
5786 
7495 

4222  4397  4572 
5958  6130  6302 
7665  7834  8002 

4746  4920  5094 
6473  6644  6815 
8171  8339  8507 

5267  5440  5613 
6985  7156  7326 
8675  8842  9009 

6.0 

9176 

9342  9509  9675 

9840  *0006  *0171 

*0336  *0500  *0665 

6.1 
6.2 
6.3 

1.8  0829 
2455 
4055 

0993  1156  1319 
2616  2777  2938 
4214  4372  4530 

1482  1645  1808 
3098  3258  3418 
4688  4845  5003 

1970  2132  2294 
3578  3737  3895 
5160  5317  6473 

6.4 
6.5 
6.6 

5630 
7180 
8707 

5786  5942  6097 
7334  7487  7641 
8858  9010  9160 

6253  6408  6563 
7794  7947  8099 
9311  9462  9612 

6718  6872  7026 
8251  8403  8555 
9762  9912*0061 

6.7 
6.8 
6.9 

1.90211 
1692 
3152 

0360  0509  0658 
1839  1986  2132 
3297  3442  3586 

0806  0954  1102 
2279  2425  2571 
3730  3874  4018 

1250  1398  1545 
2716  2862  3007 
4162  4305  4448 

7.0 

4591 

4734  4S76  5019 

5161  5303  5445 

5586  5727  5869 

7.1 
7.2 
7.3 

6009 
7408 
8787 

6150  6li91  6431 
7547  7685  7824 
8924  90t>l  9198 

6571  6711  6851 
7962  8100  8238 
9334  9470  9606 

6991  7130  7269 
8376  8513  8650 
9742  9877*0013 

7.4 
7.5 
7.6 

2.0  0148 
1490 
2815 

0283  0418  0553 
1624  1757  1890 
2946  3078  3209 

0687  0821  0956 
2022  2155  2287. 
3340  3471  3601 

1089  1223  1357 
2419  2551  2683 
3732  3862  3992 

7.7 
7.8 
7.9 

4122 
5412 
6686 

4252  4381  4511 
5540  5668  5796 
6813  6939  7065 

4640  4769  4898 
5924  6051  6179 
7191  7317  7443 

5027  5156  5284 
6306  6433  6560 
7568  7694  7819 

8.0 

7944 

8069  8194  8318 

8443  8567  8691 

8815  8939  9063 

8.1 
8.2 
8.3 

9186 
2.1  0413 
1626 

9310  9433  9556 
0535  0657  0779 
1746  1866  1986 

9679  9802  9924 
0900  1021  1142 
2106  2226  2346 

*0047  *0169  *0291 
1263  1384  1505 
2465  2585  2704 

8.4 
8.5 
8.6 

2823 
4007 
5176 

2942  3061  3180 
4124  4242  4359 
5292  5409  5524 

3298  3417  3535 
4476  4593  4710 
5640  5756  5871 

3653  3771  3889 
4827  4943  5060 
5987  6102  6217 

8.7 
8.8 
8.9 

6332 
7475 
8605 

6447  6562  6677 
7589  7702  7816 
8717  8830  8942 

6791  6905  7020 
7929  8042  8155 
9054  9165  9277 

7134  7248  7361 
8267  8380  8493 
9389  9500  9611 

9.0 

9722 

9834  9944*0055 

*0166  *0276  *0387 

*0497  *0607  *0717 

9.1 
9.2 
9.3 

2.2  0827 
1920 
3001 

0937  1047  1157 
2029  2138  2246 
3109  3216  3324 

1266  1375  1485 
2354  2462  2570 
3431  3538  3645 

1594  1703  1812 
2678  2786  2894 
3751  3858  3965 

9.4 
9.5 
9.6 

4071 
5129 
6176 

4177  4284  4390 
5234  5339  5444 
6280  6384  6488 

4496  4601  4707 
5549  5654  5759 
6592  6696  6799 

4813  4918  5024 
5863  5968  6072 
6903  7006  7109 

9.7 
9.8 
9.9 

7213 
8238 
9253 

7316  7419  7521 
8340  8442  8544 
9354  9455  9556 

7624  7727  7829 
8646  8747  8849 
9657  9757  9858 

7932  8034  8136 
8950  9051  9152 
9958  *0058  *0158 

10.0 

2.3  0259 

0358  0458  0558 

0658  0757  0857 

0956  1055  1154 

N 

0 

123 

456 

789 

114 


Napierian  or  Natural  Logarithms  —  10  to  99          [VII 


10 

2.30259 

25 

3.21888 

40 

3.68888 

55 

4.00733 

70 

4.24850 

85 

4.44265 

11 

12 
13 

14 

2.39790 
2.48491 
2.56495 
2.63906 

26 
27 
28 
29 

3.25810 
3.29584 
3.33220 
3.36730 

41 
42 
43 

44 

3.71357 
3.73767 
3.76120 
3.78419 

56 
57 
58 
59 

4.02535 
4.04305 
4.06044 
4.07754 

71 
72 
73 
74 

4.26268 
4.27667 
4.29046 
4.30407 

86 
87 
88 
89 

4.45435 
4.46591 
4.47734 
4.48864 

15 

2.70805 

30 

3.40120 

45 

3.80666 

60 

4.09434 

75 

4.31749 

90 

4.49981 

16 
17 
18 
19 

2.77259 
2.83321 
2.89037 
2.94444 

31 
32 
33 
34 

3.43399 
3.46574 
3.49651 
3.52636 

46 
47 
48 
49 

3.82864 
3.85015 
3.87120 

3.89182 

61 
62 
63 

64 

4.11087 
4.12713 
4.14313 

4.15888 

76 
77 
78 
79 

4.33073 
4.34381 
4.35671 
4.36945 

91 

92 
93 
94 

4.51086 
4.52179 
4.53260 
4.54329 

20 

2.99573 

35 

36 
37 
38 
39 

3.55535 

50 

3.91202 

65 

4.17439 

80 

4.38203 

95 

4.55388 

21 

22 
23 
24 

3.04452 
3.09104 
3.13549 
3.17805 

3.58352 
3.61092 
3.63759 
3.66356 

51 
52 
53 
54 

3.93183 
3.95124 
3.97029 
3.98898 

66 
67 
68 
69 

4.18965 
4.20469 
4.21951 
4.23411 

81 
82 
83 
84 

4.39445 
4.40672 

4.41884 
4.43082 

96 
97 
98 
99 

4.56435 
4.57471 
4.58497 
4.59512 

Napierian  or  Natural  Logarithms  — 100  to  409 


N 

0 

123 

456 

789 

10 

4.6  0517 

1512  2497  3473 

4439  5396  6344 

7283  8213  9135 

11 
12 
13 

4.7  0048 
8749 
4.8  6753 

0953  1850  2739 
9579  *0402  *1218 
7520  8280  9035 

3620  4493  5359 
*2028  *2831  *3628 
9784  *0527  *1265 

6217  7068  7912 
*4419  *5203  *5981 
*1998  *2725  *3447 

14 
15 
16 

4.9  4164 
5.0  1064 
7517 

4876  5583  6284 
1728  2388  3044 
8140  8760  9375 

6981  7673  8361 
3695  4343  4986 
9987  *0595  *1199 

9043  9721  *0395 
6625  6260  6890 
*1799  *2396  *2990 

17 
18 
19 

5.1  3580 
9296 
5.2  4702 

4166  4749  5329 
9850  *0401  *0949 
5227  5750  6269 

5906  6479  7048 
*1494  *2036  *2575 
6786  7300  7811 

7615  8178  8739 
*3111  *3644  *4175 
8320  8827  9330 

20 

9832 

*0330  *0827  *1321 

*1812  *2301  *2788 

*3272  *3754  *4233 

21 
22 
23 

5.34711 
9363 
5.4  3808 

5186  5659  6129 
9816  *0268  *0717 
4242  4674  5104 

6598  7064  7528 
*1165  *1610  *2053 
5532  5959  6383 

7990  8450  8907 
*2495  *2935  *3372 
6806  7227  7646 

24 
25 
26 

8064 
6.5  2146 
6068 

8480  8894  9306 
2545  2943  3339 
6452  6834  7215 

9717  *0126  *0533 
3733  4126  4518 
7595  7973  8350 

*0939  *1343  *1745 
4908  5296  5683 
8725  9099  9471 

27 

28 
29 

9842 
5.6  3479 
6988 

*0212  *0580  *0947 
3835  4191  4545 
7332  7675  8017 

*1313  *1677  *2040 
4897  5249  5599 
8358  8698  9036 

*2402  *2762  *3121 
6948  6296  6643 
9373  9709*0044 

30 

5.7  0378 

0711  1043  1373 

1703  2031  2359 

2685  3010  3334 

31 
32 
33 

3657 
6832 
9909 

3979  4300  4620 
7144  7455  7765 
*0212  *0513  *0814 

4939  6257  5574 
8074  8383  8690 
*1114  *1413  *1711 

5890  6205  6519 
8996  9301  9606 
*2008  *2305  *2600 

34 
35 
36 

6.8  2895 
5793 
8610 

3188  3481  3773 
6079  6363  6647 
8888  9164  9440 

4064  4354  4644 
6930  7212  7493 
9715  9990*0263 

4932  5220  5507 
7774  8053  8332 
*0536  *0808  *1080 

37 
38 
39 

6.9  1350 
4017 
6615 

1620  1889  2158 
4280  4542  4803 
6871  7126  7381 

2426  2693  2959 
5064  6324  5584 
7635  7889  8141 

3225  3489  3754 
5842  6101  6358 
8394  8645  8896 

40 

9146 

9396  9645  9894 

*0141  *0389  *0635 

*0881  *1127  *1372 

N 

0 

123 

456 

789 

Above  409,  use  the  formula     log,  lOn  =  log,  n  +  log,  10 
or  the  formula  log,  n  =  log,  10-logio  n  = 


=  loge  n  +  2.30258509, 
2.30258509  logio  n. 


vim 


Table  VIII  —  Multiples  of  M  and  of  1/M 


115 


AT 

N-M 

N 

N-M 

AT 

N  -r-  M 

N 

N  -r-M 

0 

0.00000  000 

50 

21.71472410 

0 

0.00000  000 

50 

115.12925465 

1 
2 
3 

0.43429  448 
0.86858  896 
1.30288  345 

51 
52 
53 

22.14901  858 
22.58331  306 
23.01760  754 

1 
2 
3 

2.30258  509 
4.60517  019 
6.90775  528 

51 
52 
53 

117.43183974 
119.73442484 
122.03700  993 

4 
5 
6 

1.73717  793 
2.17147241 
2.60576  689 

54 
55 
56 

23.45190  202 
23.88619  650 
24.32049  099 

4 
5 
6 

9.21034  037 
11.51292546 
13.81551  056 

54 
55 
56 

124.33959  502 
126.64218011 
128.94476  521 

7 
8 
9 

3.04006  137 
3.47435  586 
3.90865  034 

57 
58 
59 

24.75478  547 
25.18907  995 
25.62337  443 

7 

8 
9 

16.11809  565 
18.42068  074 
20.72326  584 

57 

58 
59 

131.24735  030 
133.54993  539 
135.85252  049 

10 

4.34294  482 

60 

26.05766  891 

10 

23.02585  093 

60 

138.15510558 

11 
12 
13 

4.77723  930 
5.21153378 
5.64582  826 

61 
62 
63 

26.49196  340 
26.92625  788 
27.36055  236 

11 
12 
13 

25.32843  602 
27.63102  112 
29.93360  621 

61 
62 
63 

140.45769  067 
142.76027  577 
145.06286  086 

14 
15 
16 

6.08012  275 
6.51441  723 
6.94871  171 

64 
65 
66 

27.79484  684 
28.22914  132 
28.66343  581 

14 
15 
16 

32.23619  130 
34.53877  639 
36.84136  149 

64 
65 
66 

147.36544  595 
149.66803  104 
151.97061  614 

17 
18 
19 

7.38300  619 
7.81730  067 
8.25159  516 

67 

68 
69 

29.09773  029 
29.53202  477 
29.96631  925 

17 
18 
19 

39.14394  658 
41.44653  167 
43.74911  677 

67 

68 
69 

154.27320  123 
156.57578  632 
158.87837  142 

20 

8.68588  964 

70 

30.40061  373 

20 

46.05170  186 

70 

161.18095  651 

21 
22 
23 

9.12018412 
9.55447  860 
9.98877  308 

71 
72 
73 

30.83490  822 
31.26920270 
31.70349  718 

21 
22 
23 

48.35428  695 
50.65687  205 
52.95945  714 

71 
72 
73 

163.48354  160 
165.78612  670 
168.08871  179 

24 
25 
26 

10.42306  757 
10.85736  205 
11.29165653 

74 
75 
76 

32.13779  166 
32.57208  614 
33.00638  062 

24 
25 
26 

55.26204  223 
57.56462  732 
59.86721  242 

74 
75 
76 

170.39129  688 
172.69388  197 
174.99646  707 

27 

28 
29 

11.72595  101 
12.16024  549 
12.59453  998 

77 
78 
79 

33.44067511 
33.87496  959 
34.30926  407 

27 
28 
29 

62.16979  751 
64.47238  260 
66.77496  770 

77 

78 
79 

177.29905  216 
179.60163  725 
181.90422  235 

30 

13.02883  446 

80 

34.74355  855 

30 

69.07755  279 

80 

184.20680  744 

31 
32 
33 

13.46312  894 
13.89742  342 
14.33171  790 

81 
82 
83 

35.17785  303 
35.61214752 
36.04644  200 

31 
32 
33 

71.38013  788 
73.68272  298 
75.98530  807 

81 
82 
83 

186.50939  253 
188.81197  763 
191.11456272 

34 
35 
36 

14.76601  238 
15.20030  687 
15.63460  135 

84 
85 
86 

36.48073  648 
36.91503  096 
37.34932  544 

34 
35 
36 

78.28789  316 
80.59047  825 
82.89306  335 

84 
85 
86 

193.41714  781 
195.71973  290 
198.02231  800 

37 
38 
39 

16.06889  583 
16.50319  031 
16.93748  479 

87 
88 
89 

37.78361  993 
38.21791  441 
38.65220  889 

37 
38 
39 

40~ 

85.19564  844 
87.49823  353 
89.80081  863 

87 

88 
89 

200.32490  309 
202.62748  818 
204.93007  328 

40 

17.37177  928 

90 

39.08650  337 

92.10340  372 

90 

207.23265  837 

41 
42 
43 

17.80607  376 
18.24036  824 
18.67466  272 

91 
92 
93 

39.52079  785 
39.95509  234 
40.38938  682 

41 
42 
43 

94.40598  881 
96.70857  391 
99.01115900 

91 
92 
93 

209.53524  346 
211.83782856 
214.14041  365 

44 
45 
46 

19.10895  720 
19.54325  169 
19.97754  617 

94 
95 
96 

40.82368  130 
41.25797  578 
41.69227  026 

44 
45 
46 

101.31374  409 
103.61632918 
105.91891  428 

94 
95 
96 

216.44299  874 
218.74558  383 
221.04816  893 

47 
48 
49 

20.41184  065 
20.84613  513 
21.28042  961 

97 

98 
99 

42.12656474 
42.56085  923 
42.99515  371 

47 
48 
49 

108.22149  937 
110.52408446 
112.82666956 

97 
98 
99 

223.35075  402 
225.65333911 
227.95592  421 

50 

21.71472410 

100 

43.42944  819 

50 

115.12925465 

100 

230.25S50  930 

M  =  logic  e  =  .43429  44819  03251  82765 
logio  n  =  lc>£«  n-logio  e=M  loge  n. 
logio  <?  =z-logio  e  =x-M. 


1/M  =  log,  10  =2.30258  50929  94045  68402 
loge  n  =  logio  n-loge  10  =  (1/M)  logio  n. 
logt  (10n-x) 


116        Table  IX  —  Logarithms  of  Hyperbolic  Functions         [IX 


X 

e* 

Value       Logio 

e~x 

Value 

Sinh  x 

Value  Logio 

Cosh  x 

Value       Logio 

Tanh* 

Value 

0.00 

1.0000      .00000 

1.0000 

0.0000  -  co 

1.0000      .00000 

.00000 

0.01 
0.02 
0.03 

1.0101      .00434 
1.0202      .00869 
1.0305      .01303 

.99005 
.98020 
.97045 

0.0100  .00001 
0.0200  .30106 
0.0300  .47719 

1.0001      .00002 
1.0002      .00009 
1.0005      .00020 

.01000 
.02000 
.02999 

0.04 
0.05 
0.06 

1.0408      .01737 
1.0513      .02171 
1,0618     .02606 

.96079 
.95123 
.94176 

0.0400  .60218 
0.0500  .69915 
0.0600  .77841 

1.0008      .00035 
1.0013      .00054 
1.0018      .00078 

.03998 
.04996 
.05993 

0.07 
0.08 
0.09 

1.0725      .03040 
1.0833      .03474 
1.0942      .03909 

.93239 
.92312 
.91393 

0.0701  .84545 
0.0801  .90355 
0.0901  .95483 

1.0025      .00106 
1.0032      .00139 
1.0041      .00176 

.06989 
.07983 
.08976 

0.10 

1.1052      .04343 

.90484 

0.1002  .00072 

1.0050      .00217 

.09967 

0.11 
0.12 
0.13 

1.1163      .04777 
1.1275      .05212 
1.1388      .05646 

.89583 
.88692 
.87810 

0.1102  .04227 
0.1203  .08022 
0.1304  .11517 

1.0061      .00262 
1.0072      .00312 
1.0085      .00366 

.10956 
.11943 
.12927 

0.14 
0.15 
0.16 

1.1503      .06080 
1.1618      .06514 
1.1735      .06949 

.86936 
.86071 
.85214 

0.1405  .14755 
0.1506  .17772 
0.1607  .20597 

1.0098      .00424 
1.0113      .00487 
1.0128      .00554 

.13909 
.14889 
.15865 

0.17 

0.18 
0.19 

1.1853     .07383 
1.1972     .07817 
1.2092      .08252 

.84366 
.83527 
.82696 

0.1708  .23254 
0.1810  .25762 
0.1911  .28136 

1.0145      .00625 
1.0162      .00700 
1.0181      .00779 

.16838 
.17808 
.18775 

0.20 

1.2214      .08686 

.81873 

0.2013  .30392 

1.0201      .00863 

.19738 

0.21 
0.22 
0.23 

1.2337      .09120 
1.2461      .09554 
1.2586      .09989 

.81058 
.80252 
.79453 

0.2115  .32541 
0.2218  .34592 
0.2320  .36555 

1.0221      .00951 
1.0243      .01043 
1.0266      .01139 

.20697 
.21652 
.22603 

0.24 
0.25 
0.26 

1.2712      .10423 
1.2840      .10857 
1.2969      .11292 

.78663 
.77880 
.77105 

0.2423  .38437 
0.2526  .40245 
0.2629  .41986 

1.0289      .01239 
1.0314      .01343 
1.0340      .01452 

.23550 
.24492 
.25430 

0.27 
0.28 
0.29 

1.3100      .11726 
1.3231      .12160 
1.3364      .12595 

.76338 
.75578 

.74826 

0.2733  .43663 
0.2837  .45282 
0.2941  .46847 

1.0367     .01564 
1.0395      .01681 
1.0423      .01801 

.26362 
.27291 
.28213 

0.30 

1.3499      .13029 

.74082 

0.3045  .48362 

1.0453      .01926 

.29131 

0.31 
0.32 
0.33 

1.3634      .13463 
1.3771      .13897 
1.3910      .14332 

.73345 
.72615 
.71892 

0.3150  .49830 
0.3255  .51254 
0.3360  .52637 

1.0484      .02054 
1.0516      .02187 
1.0549      .02323 

.30044 
.30951 
.31852 

0.34 
0.35 
0.36 

1.4049      .14766 
1.4191      .15200 
1.4333      .15635 

.71177 
.70469 
.69768 

0.3466  .53981 
0.3572  .55290 
0.3678  .56564 

1.0584      .02463 
1.0619      .02607 
1.0655      .02755 

.32748 
.33638 
.34521 

0.37 
0.38 
0.39 

1.4477      .16069 
1.4623      .16503 
1.4770      .16937 

.69073 
.68386 
.67706 

0.3785  .57807 
0.3892  .59019 
0.4000  .60202 

1.0692      .02907 
1.0731      .03063 
1.0770      .03222 

.35399 
.36271 
.37136 

0.40 

1.4918      .17372 

.67032 

0.4108  .61358 

1.0811      .03385 

.37995 

0.41 
0.42 
0.43 

1.5068      .17806 
1.5220     .18240 
1.5373      .18675 

.66365 
.65705 
.65051 

0.4216  .62488 
0.4325  .63594 
0.4434  .64677 

1.0852      .03552 
1.0895      .03723 
1.0939      .03897 

.38847 
.39693 
.40532 

0.44 
0.45 
0.46 

1.5527     .19109 
1.5683      .19543 
1.5841      .19978 

.64404 
.63763 
.63128 

0.4543  .65738 
0.4653  .66777 
0.4764  .67797 

1.0984     .04075 
1.1030      .04256 
1.1077      .04441 

.41364 
.42190 
.43008 

0.47 
0.48 
0.49 

1.6000      .20412 
1.6161      .20846 
1.6323      .21280 

.62500 
.61878 
.61263 

0.4875  .68797 
0.4986  .69779 
0.5098  .70744 

1.1125      .04630 
1.1174      .04822 
1.1225      .05018 

.43820 
.44624 
.45422 

0.50 

1.0487      .21715 

.60653 

0.5211  .71692 

1.1276      .05217 

.46212 

IX]         Values  and  Logarithms  of  Hyperbolic  Functions         117 


X 

e* 

Value  Logio 

e~x 

Value 

Sinh  .v 
Value       Logio 

Cosh* 

Value  Logio 

Tanh  x 
Value 

0.50 

1.6487  .21715 

.60653 

0.5211      .71692 

1.1276  .05217 

.46212 

0.51 
0.52 
0.53 

1.6653  .22149 
1.6820  52583 
1.6989  53018 

.60050 
.59452 
.58860 

0.5324      .72624 
0.5438      .73540 
0.5552      .74442 

1.1329  .05419 
1.1383  .05625 
1.1438  .05834 

.46995 
.47770 
.48538 

0.54 
0.55 
0.56 

1.7160  .23452 
1.7333  .23886 
1.7507  54320 

.58275 
.57695 
.57121 

0.5666      .75330 
0.5782      .76204 
0.5897      .77065 

1.1494  .06046 
1.1551  .06262 
1.1609  .06481 

.49299 
.50052 
.50798 

0.57 
0.58 
0.59 

1.7683  54755 
1.7860  55189 
1.8040  .25623 

.56553 
.55990 
.55433 

0.6014      .77914 
0.6131      .78751 
0.6248      .79576 

1.1669  .06703 
1.1730  .06929 
1.1792  .07157 

.51536 
.52267 
.52990 

0.60 

1.8221  .26058 

.54881 

0.6367      .80390 

1.1855  .07389 

.53705 

0.61 
0.62 
0.63 

1.8404  56492 
1.8589  56926 
1.8776  57361 

.54335 
.53794 
.53259 

0.6485      .81194 
0.6605      .81987 
0.6725     .82770 

1.1919  .07624 
1.1984  .07861 
1.2051  .08102 

.54413 
.55113 
.55805 

0.64 
0.65 
0.66 

1.8965  57795 
1.9155  58229 
1.9348  58663 

.52729 
.52205 
.51685 

0.6846     .83543 
0.6967      .84308 
0.7090      .85063 

1.2119  .08346 
1.2188  .08593 
1.2258  .08843 

.56490 
.57167 
.57836 

0.67 
0.68 
0.69 

1.9542  59098 
1.9739  59532 
1.9937  59966 

.51171 
.50662 
.50158 

0.7213      .85809 
0.7336     .86548 
0.7461      .87278 

1.2330  .09095 
1.2402  .09351 
1.2476  .09609 

.58498 
.59152 
.59798 

0.70 

2.0138  .30401 

.49659 

0.7586     .88000 

1.2552  .09870 

.60437 

0.71 
0.72 
0.73 

2.0340  .30835 
2.0544  .31269 
2.0751  .31703 

.49164 
.48675 
.48191 

0.7712      .88715 
0.7838     .89423 
0.7966      .90123 

15628  .10134 
1.2706  .10401 
1.2785  .10670 

.61068 
.61691 
.62307 

0.74 
0.75 
0.76 

2.0959  .32138 
2.1170  .32572 
2.1383  .33006 

.47711 
.47237 
.46767 

0.8094      .90817 
0.8223      .91504 
0.8353      .92185 

1.2865  .10942 
1.2947  .11216 
1.3030  .11493 

.62915 
.63515 
.64108 

0.77 
0.78 
0.79 

2.1598  .33441 
2.1815  .33875 
2.2034  .34309 

.46301 
.45841 
.45384 

0.8484      .92859 
0.8615      .93527 
0.8748      .94190 

1.3114  .11773 
1.3199  .12055 
1.3286  .12340 

.64693 
.65271 
.65841 

0.80 

2.2255  .34744 

.44933 

0.8881      .94846 

1.3374  .12627 

.66404 

0.81 
0.82 
0.83 

2.2479  .35178 
2.2705  .35612 
2.2933  .36046 

.44486 
.44043 
.43605 

0.9015      .95498 
0.9150      .96144 
0.9286      .96784 

1.3464  .12917 
1.3555  .13209 
1.3647  .13503 

.66959 
.67507 
.68048 

0.84 
0.85 
0.86 

2.3164  .36481 
2.3396  .36915 
2.3632  .37349 

.43171 
.42741 
.42316 

0.9423      .97420 
0.9561      .98051 
0.9700     .98677 

1.3740  .13800 
1.3835  .14099 
1.3932  .14400 

.68581 
.69107 
.69626 

0.87 
0.88 
0.89 

2.3869  .37784 
2.4109  .38218 
2.4351  .38652 

.41895 
.41478 
.41066 

0.9840      .99299 
0.9981      .99916 
1.0122      .00528 

1.4029  .14704 
1.4128  .15009 
1.4229  .15317 

.70137 
.70642 
.71139 

0.90 

2.4596  .39087 

.40657 

1.0265      .01137 

1.4331  .15627 

.71630 

0.91 
0.92 
0.93 

2.4843  .39521 
2.5093  .39955 
2.5345  .40389 

.40252 
.39852 
.39455 

1.0409      .01741 
1.0554      .02341 
1.0700      .02937 

1.4434  .15939 
1.4539  .16254 
1.4645  .16570 

.72113 
.72590 
.73059 

0.94 
0.95 
0.96 

2.5600  .40824 
2.5857  .41258 
2.6117  .41692 

.39063 
.38674 
.38289 

1.0847      .03530 
1.0995      .04119 
1.1144      .04704 

1.4753  .16888 
1.4862  .17208 
1.4973  .17531 

.73522 
.73978 
.74428 

0.97 
0.98 
0.99 

2.6379  .42127 
2.6645  .42561 
2,6912  .42995 

.37908 
.37531 
.37158 

1.1294      .05286 
1.1446      .05864 
1.1598      .06439 

1.5085  .17855 
1.5199  .18181 
1.5314  .18509 

.74870 
.75307 
.75736 

1.00 

2.7183  .43429 

.36788 

1.1752      .07011 

1.5431  .1SS3'J 

.76159 

118         Values  and  Logarithms  of  Hyperbolic  Functions         [IX 


X 

e* 
Value        Logic 

e~^ 
Value 

Sinh  x 

Value        Logio 

Cosh  x 

Value       Logio 

Tanh* 

Value 

1.00 

2.7183      .43429 

.36788 

1.1752      .07011 

1.5431      .18839 

.76159 

1.01 
1.02 
1.03 

2.7456      .43864 
2.7732      .44298 
2.8011      .44732 

.36422 
.36060 
.35701 

1.1907      .07580 
1.2063      .08146 
1.2220      .08708 

1.5549      .19171 
1.5669      .19504 
1.5790      .19839 

.76576 
.76987 
.77391 

1.04 
1.05 
1.06 

2.8292      .45167 
2.8577      .45601 
2.8864      .46035 

.35345 
.34994 
.34646 

1.2379      .09268 
1.2539      .09825 
1.2700      .10379 

1.5913      .20176 
1.6038      .20515 
1.6164      .20855 

.77789 
.78181 
.78566 

1.07 
1.08 
1.09 

2.9154      .46470 
2.9447      .46904 
2.97*3      .47338 

.34301 
.33960 
.33622 

1.2862      .10930 
1.3025      .11479 
1.3190      .12025 

1.6292      .21197 
1.6421      .21541 
1.6552      .21886 

.78946 
.79320 
.79688 

1.10 

3.0042      .47772 

.33287 

1.3356      .12569 

1.6685      .22233 

.80050 

1.11 
1.12 
1.13 

3.0344      .48207 
3.0649      .48641 
3.0957      .49075 

.32956 
.32628 
.32303 

1.3524      .13111 
1.3693      .13649 
1.3863      .14186 

1.6820      .22582 
1.6956      .22931 
1.7093      .23283 

.80406 
.80757 
.81102 

1.14 
1.15 
1.16 

3.1268      .49510 
3.1582      .49944 
3.1899      .50378 

.31982 
.31664 
.31349 

1.4035      .14720 
1.4208      .15253 
1.4382      .15783 

1.7233      .23636 
1.7374      .23990 
1.7517      .24346 

.81441 
.81775 
.82104 

1.17 
1.18 
1.19 

3.2220      .50812 
3.2544      .51247 
3.2871      .51681 

.31037 

.30728 
.30422 

1.4558      .16311 
1.4735      .16836 
1.4914      .17360 

1.7662      .24703 
1.7808      .25062 
1.7957      .25422 

.82427 
.82745 
.83058 

1.20 

3.3201      .52115 

.30119 

1.5095      .17882 

1.8107      .25784 

.83365 

1.21 
1.22 
1.23 

3.3535      .52550 
3.3872      .52984 
3.4212      .53418 

.29820 
.29523 
.29229 

1.5276      .18402 
1.5460      .18920 
1.5645      .19437 

1.8258      .26146 
1.8412      .26510 
1.8568      .26876 

.83668 
.83965 
.84258 

1.24 
1.25 
1.26 

3.4556      .53853 
3.4903      .54287 
3.5254      .54721 

.28938 
.28650 
.28365 

1.5831      .19951 
1.6019      .20464 
1.6209      .20975 

1.8725      .27242 
1.8884      .27610 
1.9045      .27979 

.84546 
.84828 
.85106 

1.27 

1.28 
1.29 

3.5609      .55155 
3.5966      .55590 
3.6328      .56024 

.28083 
.27804 
.27527 

1.6400      .21485 
1.6593      .21993 
1.6788      .22499 

1.9208      .28349 
1.9373      .28721 
1.9540      .29093 

.85380 

.85648 
.85913 

1.30 

3.6693      .56458 

.27253 

1.6984      .23004 

1.9709      .29467 

.86172 

1.31 
1.32 
1.33 

3.7062      .56893 
3.7434      .57327 
3.7810      .57761 

.26982 
.26714 
.26448 

1.7182      .23507 
1.7381      .24009 
1.7583      .24509 

1.9880      .29842 
2.0053      .30217 
2.0228      .30594 

.86428 
.86678 
.86925 

1.34 
1.35 
1.36 

3.8190      .58195 
3.8574      .58630 
3.8962      .59064 

.26185 
.25924 
.25666 

1.7786      .25008 
1.7991      .25505 
1.8198      .26002 

2.0404      .30972 
2.0583      .31352 
2.0764      .31732 

.87167 
.87405 
.87639 

1.37 
1.38 
1.39 

3.9354      .59498 
3.9749      .59933 
4.0149      .60367 

.25411 
.25158 
.24908 

1.8406      .26496 
1.8617      .26990 
1.8829      .27482 

2.0947      .32113 
2.1132      .32495 
2.1320      .32878 

.87869 
.88095 
.88317 

1.40 

4.0552      .60801 

.24660 

1.9043      .27974 

2.1509      .33262 

.88535 

1.41 
1.42 
1.43 

4.0960      .61236 
4.1371      .61670 
4.1787      .62104 

.24414 
.24171 
.23931 

1.9259      .28464 
1.9477      .28952 
1.9697      .29440 

2.1700      .33647 
2.1894      .34033 
2.2090      .34420 

.88749 
.88960 
.89167 

1.44 
1.45 
1.46 

4.2207      .62538 
4.2631      .62973 
4.3060      .63407 

.23693 
.23457 
.23224 

1.9919      .29926 
2.0143      .30412 
2.0369      .30896 

2.2288      .34807 
2.2488      .35196 
2.2691      .35585 

.89370 
.89569 
.89765 

1.47 

1.48 
1.49 

4.3492      .63841 
4.3929      .64276 
4.4371      .64710 

.22993 
.22764 
.22537 

2.0597      .31379 
2.0827      .31862 
2.1059      .32343 

2.2896      .35976 
2.3103      .36367 
2.3312      .36759 

.89958 
.90147 
.90332 

1.50 

4.4817      .65144 

.22313 

2.1293      .32823 

2.3524      .37151 

.90515 

IX]         Values  and  Logarithms  of  Hyperbolic  Functions        119 


X 

e* 

Value       Logio 

e"1 

Value 

Sinh* 

Value       Logio 

Cosh  x 

Value       Logio 

Tanh* 

Value 

1.50 

4.4817      .65144 

.22313 

2.1293      .32823 

2.3524      .37151 

.90515 

1.51 
1.52 
1.53 

4.5267      .65578 
4.5722      .66013 
4.6182      .66447 

.22091 
.21871 
.21654 

2.1529      .33303 
2.1768     .33781 
2.2008      .34258 

2.3738      .37545 
2.3955      .37939 
2.4174      .38334 

.90694 
.90870 
.91042 

1.54 
1.55 
1.56 

4.6646      .66881 
4.7115      .67316 
4.7588      .67750 

.21438 
.21225 
.21014 

2.2251      .34735 
2.2496      .35211 
2.2743      .35686 

2.4395     .38730 
2.4619      .39126 
2.4845      .39524 

.91212 
.91379 
.91542 

1.57 
1.58 
1.59 

4.8066      .68184 
4.8550      .68619 
4.9037     .69053 

.20805 
.20598 
.20393 

2.2993     .36160 
2.3245      .36633 
2.3499      .37105 

2.5073      .39921 
2.5305      .40320 
2.5538     .40719 

.91703 
.91860 
.92015 

1.60 

4.9530      .69487 

.20190 

2.3756      .37577 

2.5775      .41119 

.92167 

1.61 
1.62 
1.63 

5.0028     .69921 
5.0531      .70356 
5.1039      .70790 

.19989 
.19790 
.19593 

2.4015      .38048 
2.4276      .38518 
2.4540      .38987 

2.6013      .41520 
2.6255      .41921 
2.6499     .42323 

.92316 
.92462 
.92606 

1.64 
1.65 
1.66 

5.1552     .71224 
5.2070     .71659 
5.2593     .72093 

.19398 
.19205 
.19014 

2.4806      .39456 
2.5075     .39923 
2.5346     .40391 

2.6746     .42725 
2.6995      .43129 
2.7247      .43532 

.92747 
.92886 
.93022 

1.67 
1.68 
1.69 

5.3122     .72527 
5.3656     .72961 
5.4195      .73396 

.18825 
.18637 
.18452 

2.5620     .40857 
2.5896      .41323 
2.6175      .41788 

2.7502      .43937 
2.7760      .44341 
2.8020      .44747 

.93155 

.93286 
.93415 

1.70 

5.4739      .73830 

.18268 

2.6456      .42253 

2.8283      .45153 

.93541 

1.71 
1.72 
1.73 

5.5290      .74264 
5.5845      .74699 
5.6407     .75133 

.18087 
.17907 
.17728 

2.6740      .42717 
2.7027     .43180 
2.7317     .43643 

2.8549      .45559 
2.8818      .45966 
2.9090     .46374 

.93665 
.93786 
.93906 

1.74 
1.75 
1.76 

5.6973     .75567 
5.7546     .76002 
5.8124      .76436 

.17552 
.17377 
.17204 

2.7609      .44105 
2.7904     .44567 
2.8202      .45028 

2.9364     .46782 
2.9642      .47191 
2.9922      .47600 

.94023 
.94138 
.94250 

1.77 
1.78 
1.79 

5.8709     .76870 
5.9299      .77304 
5.9895      .77739 

.17033 

.16864 
.16696 

2.8503      .45488 
2.8806      .45948 
2.9112      .46408 

3.0206     .48009 
3.0492      .48419 
3.0782      .48830 

.94361 
.94470 
.94576 

1.80 

6.0496      .78173 

.16530 

2.9422      .46867 

3.1075      .49241 

.94681 

1.81 
1.82 
1-83 

6.1104     .78607 
6.1719     .79042 
6.2339     .79476 

.16365 
.16203 
.16041 

2.9734      .47325 
3.0049     .47783 
3.0367     .48241 

3.1371      .49652 
3.1669      .50064 
3.1972      .50476 

.94783 
.94884 
.94983 

1.84 
1.85 
1.86 

6.2965     .79910 
6.3598      .80344 
6.4237     .80779 

.15882 
.15724 
.15567 

3.0689     .48698 
3.1013      .49154 
3.1340     .49610 

3.2277     .50889 
3.2585     .51302 
3.2897     .51716 

.95080 
.95175 
.95268 

1.87 
1.88 
1.89 

6.4883     .81213 
6.5535     .81647 
6.6194      .82082 

.15412 
.15259 
.15107 

3.1671      .50066 
3.2005      .50521 
3.2341      .50976 

3.3212      .52130 
3.3530      .52544 
3.3852      .52959 

.95359 
.95449 
.95537 

1.90 

6.6859      .82516 

.14957 

3.2682      .51430 

3.4177      .53374 

.95624 

1.91 
1.92 
1.93 

6.7531      .82950 
6.8210     .83385 
6.8895      .83819 

.14808 
.14661 
.14515 

3.3025      .51884 
3.3372      .52338 
3.3722      .52791 

3.4506      .53789 
3.4838      .54205 
3.5173      .54621 

.95709 
.95792 
.95873 

1.94 
1.95 
1.96 

6.9588     .84253 
7.0287      .84687 
7.0993     .85122 

.14370 
.14227 
.14086 

3.4075      .53244 
3.4432      .53696 
3.4792      .54148 

3.5512      .55038 
3.5855      .55455 
3.6201      .55872 

.95953 
.96032 
.96109 

1.97 
1.98 
1.99 

7.1707     .85556 
7.2427      .85990 
7.3155      .86425 

.13946 
.13807 
.13670 

3.5156      .54600 
3.5523      .55051 
3.5894      .55502 

3.6551      .56290 
3.6904      .56707 
3.7261      .57126 

.96185 
.96259 
.96331 

2.00 

7.3891      .86859 

.13534 

3.6269      .55953 

3.7622      .57544 

.96403 

120        Values  and  Logarithms  of  Hyperbolic  Functions         [IX 


X 

e* 

Value       Logio 

e-^ 

Value 

Sinh* 

Value       Logio 

Cosh  x 

Value       Logio 

Tanh* 

Value 

2.00 

7.3891      .86859 

.13534 

3.6269      .55953 

3.7622      .57514 

.96403 

2.01 
2.02 
2.03 

7.4633      .87293 
7.5383      .87727 
7.6141      .88162 

.13399 
.13266 
.13134 

3.6647      .56403 
3.7028      .56853 
3.7414      .57303 

3.7987      .57963 
3.8355      .58382 
3.8727      .58802 

.96473 
.96541 
.96609 

2.04 
2.05 
2.06 

7.6906     .88596 
7.7679      .89030 
7.8460      .89465 

.13003 
.12873 
.12745 

3.7803      .57753 
3.8196      .58202 
3.8593      .58650 

3.9103      .59221 
3.9483      .59641 
3.9867      .60061 

.96675 
.96740 
.96803 

2.07 
2.08 
2.09 

7.9248      .89899 
8.0045      .90333 
8.0849      .90768 

.12619 
.12493 
.12369 

3.8993      .59099 
3.9398      .59547 
3.9806      .59995 

4.0255      .60482 
4.0647      .60903 
4.1043      .61324 

.96865 
.96926 
.96986 

2.10 

8.1662      .91202 

.12246 

4.0219      .60443 

4.1443      .61745 

.97045 

2.11 
2.12 
2.13 

8.2482      .91636 
8.3311      .92070 
8.4149      .92505 

.12124 
.12003 

.11884 

4.0635      .60890 
4.1056      .61337 
4.1480      .61784 

4.1847      .62167 
4.2256      .62589 
4.2669      .63011 

.97103 
.97159 
.97215 

2.14 
2.15 
2.16 

8.4994      .92939 
8.5849      .93373 
8.6711      .93808 

.11765 
.11648 
.11533 

4.1909      .62231 
4.2342      .62677 
4.2779      .63123 

4.3085      .63433 
4.3507      .63856 
4.3932      .64278 

.97269 
.97323 
.97375 

2.17 
2.18 
2.19 

8.7583      .94242 
8.8463      .94676 
8.9352      .95110 

.11418 
.11304 
.11192 

4.3221      .63569 
4.3666      .64015 
4.4116      .64460 

4.4362      .64701 
4.4797      .65125 
4.5236      .65548 

.97426 
.97477 
.97526 

2.20 

9.0250      .95545 

.11080 

4.4571      .64905 

4.5679      .65972 

.97574 

2.21 
2.22 
2.23 

9.1157      .95979 
9.2073      .96413 
9.2999      .96848 

.10970 
.10861 
.10753 

4.5030      .65350 
4.5494      .65795 
4.5962      .66240 

4.6127      .66396 
4.6580      .66820 
4.7037      .67244 

.97622 
.97668 
.97714 

2.24 
2.25 
2.26 

9.3933      .97282 
9.4877      .97716 
9.5831      .98151 

.10646 
.10540 
.10435 

4.6434     .66684 
4.6912      .67128 
4.7394      .67572 

4.7499      .67668 
4.7966      .68093 
4.8437      .68518 

.97759 
.97803 
.97846 

2.27 
2.28 
2.29 

9.6794      .98585 
9.7767      .99019 
9.8749      .99453 

.10331 
.10228 
.10127 

4.7880      .68016 
4.8372      .68459 
4.8868      .68903 

4.8914      .68943 
4.9395      .69368 
4.9881      .69794 

.97888 
.97929 
.97970 

2.30 

9.9742      .99888 

.10026 

4.9370      .09346 

5.0372      .70219 

.98010 

2.31 
2.32 
2.33 

10.074      .00322 
10.176      .00756 
10.278      .01191 

.09926 
.09827 
.09730 

4.9876      .69789 
5.0387      .70232 
5.0903      .70675 

5.0868      .70645 
5.1370      .71071 
5.1876      .71497 

.98049 
.98087 
.98124 

2.34 
2.35 
2.36 

10.381      .01625 
10.486      .02059 
10.591      .02493 

.09633 
.09537 
.09442 

5.1425      .71117 
5.1951      .71559 
5.2483      .72002 

5.2388      .71923 
5.2905      .72349 
5.3427      .72776 

.98161 
.98197 
.98233 

2.37 
2.38 
2.39 

10.697      .02928 
10.805      .03362 
10.913      .03796 

.09348 
.09255 
.09163 

5.3020      .72444 
5.3562      .72885 
5.4109      .73327 

5.3954     .73203 
5.4487      .73630 
5.5026      .74056 

.98267 
.98301 
.98335 

2.40 

11.023      .04231 

.09072 

5.4662      .73769 

5.5569      .74484 

.98367 

2.41 
2.42 
2.43 

11.134      .04665 
11.246      .05099 
11.359      .05534 

.08982 
.08892 
.08804 

5.5221      .74210 
5.5785      .74652 
5.6354      .75093 

5.6119      .74911 
5.6674      .75338 
5.7235      .75766 

.98400 
.98431 
.98462 

2.44 

2.45 
2.46 

11.473      .05968 
11.588      .06402 
11.705      .06836 

.08716 
.08629 
.08543 

5.6929      .75534 
5.7510      .75975 
5.8097      .76415 

5.7801      .76194 
5.8373      .76621 
5.8951      .77049 

.98492 
.98522 
.98551 

2.47 

2.48 
2.49 

11.822      .07271 
11.941      .07705 
12.061      .08139 

.08458 
.08374 
.08291 

5.8689      .76856 
5.9288      .77296 
5.9892      .77737 

5.9535      .77477 
6.0125      .77906 
6.0721      .78334 

.98579 
.98607 
.98635 

2.50 

12.182      .08574 

.08208 

6.0502      .78177 

6.1323      .78762 

.98661 

DC]         Values  and  Logarithms  of  Hyperbolic  Functions         121 


X 

e* 

Value  Logio 

*•• 
Value 

Sinh.r 
Value       Logic 

Cosh  x 

Value       Log™ 

Tanh* 

Value 

2.50 

12.182  .08574 

.08208 

6.0502      .78177 

6.1323      .78762 

.98661 

2.51 
2.52 
2.53 

12.305  .09008 
12.429  .09442 
12.554  .09877 

.08127 
.08046 
.07966 

6.1118      .78617 
6.1741      .79057 
6.2369      .79497 

6.1931      .79191 
6.2545      .79619 
6.3166     .80048 

.98688 
.98714 
.98739 

2.54 
2.55 
2.56 

12.680  .10311 
12.807  .10745 
12.936  .11179 

.07887 
.07808 
.07730 

6.3004     .79937 
6.3645      .80377 
6.4293      .80816 

6.3793     .80477 
6.4426      .80906 
6.5066      .81335 

.98764 
.98788 
.98812 

2.57 

2.58 
2.59 

13.066  .11614 
13.197  .12048 
13.330  .12482 

.07654 
.07577 
.07502 

6.4946      .81256 
6.5607      .81695 
6.6274      .82134 

6.5712     .81764 
6.6365     .82194 
6.7024      .82623 

.98835 
.98858 

.98881 

2.60 

13.464  .12917 

.07427 

6.6947      .82573 

6.76CO      .83052 

.98903 

2.61 
2.62 
2.63 

13.599  .13351 
13.736  .13785 
13.874  .14219 

.07353 
.07280 
.07208 

6.7628      .83012 
6.8315      .83451 
6.9008     .83890 

6.8363      .83482 
6.9043     .83912 
6.9729      .84341 

.98924 
.98946 
.98966 

2.64 
2.65 
2.66 

14.013  .14654 
14.154  .15088 
14.296  .15522 

.07136 
.07065 
.06995 

6.9709      .84329 
7.0417      .84768 
7.1132      .85206 

7.0423     .84771 
7.1123      .85201 
7.1831      .85631 

.98987 
.99007 
.99026 

2.67 
2.68 
2.69 

14.440  .15957 
14.585  .16391 
14.732  .16825 

.06925 
.06856 

.06788 

7.1854      .85645 
7.2583     .86083 
7.3319      .86522 

7.2546     .86061 
7.3268      .86492 
7.3998      .86922 

.99045 
.99064 
.99083 

2.70 

14.880  .17260 

.06721 

7.4063      .86960 

7.4735      .87352 

.99101 

2.71 
2.72 
2.73 

15.029  .17694 
15.180  .18128 
15.333  .18562 

.06654 
.06587 
.06522 

7.4814      .87398 
7.5572     .87836 
7.6338     .88274 

7.5479      .87783 
7.6231      .88213 
7.6991      .88644 

.99118 
.99136 
.99153 

2.74 
2.75 
2.76 

15.487  .18997 
15.643  .19431 
15.800  .19865 

.06457 
.06393 
.06329 

7.7112     .88712 
7.7894      .89150 
7.8683      .89588 

7.7758     .89074 
7.8533      .89505 
7.9316     .89936 

.99170 
.99186 
.99202 

2.77 
2.78 
2.79 

15.959  .20300 
16.119  .20734 
16.281  .21168 

.06266 
.06204 
.06142 

7.9480      .90026 
8.0285      .90463 
8.1098      .90901 

8.0106     .90367 
8.0905     .90798 
8.1712      .91229 

.99218 
.99233 

.99248 

2.80 

16.445  .21602 

.06081 

8.1919      .91339 

8.2527      .91660 

.99263 

2.81 
2.82 
2.83 

16.610  .22037 
16.777  .22471 
16.945  .22905 

.06020 
.05961 
.05901 

8.2749      .91776 
8.3586      .92213 
8.4432      .92651 

8.3351      .92091 
8.4182      .92522 
8.5022      .92953 

.99278 
.99292 
.99306 

2.84 
2.85 
2.86 

17.116  .23340 
17.288  .23774 
17.462  .24208 

.05843 
.05784 
.05727 

8.5287      .93088 
8.6150      .93525 
8.7021      .93963 

8.5871      .93385 
8.6728     .93816 
8.7594      .94247 

.99320 
.99333 
.99346 

2.87 
2.88 
2.89 

17.637  .24643 
17.814  .25077 
17.993  .25511 

.05670 
.05613 
.05558 

8.7902      .94400 
8.8791      .94837 
8.9689      .95274 

8.8469     .94679 
8.9352      .95110 
9.0244      .95542 

.99359 
.99372 

.99384 

2.90 

18.174  .25945 

.05502 

9.0596      .95711 

9.1146      .95974 

.99396 

2.91 
2.92 
2.93 

18.357  .26380 
18.541  .26814 
18.728  .27248 

.05448 
.05393 
.05340 

9.1512      .96148 
9.2437      .96584 
9.3371      .97021 

9.2056      .96405 
9.2976      .96837 
9.3905      .97269 

.99408 
.99420 
.99431 

2.94 
2.95 
2.96 

18.916  .27683 
19.106  .28117 
19.298  .28551 

.05287 
.05234 
.05182 

9.4315      .97458 
9.5268      .97895 
9.6231      .98331 

9.4844     .97701 
9.5791      .98133 
9.6749      .98565 

.99443 
.99454 
.99464 

2.97 
2.98 
2.99 

19.492  .28985 
19.688  .29420 
19.886  .29854 

.05130 
.05079 
.05029 

9.7203      .98768 
9.8185      .99205 
9.9177      .99641 

9.7716     .98997 
9.8693      .99429 
9.9680      .99861 

.99475 
.99485 
.99496 

3.00 

20.086  .30288 

.0497ft 

10.018      .00078 

10.068      .00293 

.09505 

122        Values  and  Logarithms  of  Hyperbolic  Functions         [IX 


X 

e* 

Value       Logw 

e-^ 

Value 

Sinh* 

Value       Logw 

Cosh  x 

Value       Logio 

Tanh* 

Value 

3.00 

20.086      .30288 

.04979 

10.018      .00078 

10.068      .00293 

.99505 

3.05 
3.10 
3.15 

21.115      .32460 
22.198      .34631 
23.336      .36803 

.04736 
.04505 
.04285 

10.534      .02259 
11.076      .04440 
11.647      .06620 

10.581      .02454 
11.122      .04616 
11.689     .06779 

.99552 
.99595 
.99633 

3.20 
3.25 
3.30 

24.533     .38974 
25.790      .41146 
27.113      .43317 

.04076 
.03877 
.03688 

12.246      .08799 
12.876      .10977 
13.538      .13155 

12.287      .08943 
12.915      .11108 
13.575      .13273 

.99668 
.99700 
.99728 

3.35 
3.40 
3.45 

28.503     .45489 
29.964      .47660 
31.500     .49832 

.03508 
.03337 
.03175 

14.234     .15332 
14.965      .17509 
15.734      .19685 

14.269     .15439 
14.999     .17605 
15.766      .19772 

.99754 
.99777 
.99799 

3.50 

33.115      .52003 

,03020 

16.543      .21860 

16.573      .21940 

.99818 

3.55 
3.60 
3.65 

34.813      .54175 
36.598     .56346 
38.475      .58517 

.02872 
.02732 
.02599 

17.392      .24036 
18.285      .26211 
19.224=      .28385 

17.421      .24107 
18.313      .26275 
19.250      .28444 

.99835 
.99851 
.99865 

3.70 
3.75 
3.80 

40.447     .60689 
42.521      .62860 
44.701      .65032 

.02472 
.02352 
.02237 

20.211      .30559 
21.249      .32733 
22.339      .34907 

20.236      .30612 
21.272      .32781 
22.362      .34951 

.99878 
.99889 
.99900 

3.85 
3.90 
3.95 

46.993      .67203 
49.402      .69375 
51.935      .71546 

.02128 
.02024 
.01925 

23.486     .37081 
24.691      .39254 
25.958      .41427 

23.507     .37120 
24.711      .39290 
25.977      .41459 

.99909 
.99918 
.99926 

4.00 

54.598      .73718 

.01832 

27.290      .43600 

27.308      .43629 

.99933 

4.10 
4.20 
4.30 

60.340      .78061 
66.686      .82404 
73.700     .86747 

.01657 
.01500 
.01357 

30.162      .47946 
33.336      .52291 
30.S43      .56636 

30.178     .47970 
33.351      .52310 
36.857      .56652 

.99945 
.99955 
.99963 

4.40 
4.50 
4.60 

81.451      .91090 
90.017      .95433 
99.484      .99775 

.01228 
.01111 
.01005 

40.719     .60980 
45.003      .65324- 
49.737      .69668 

40.732      .60993 
45.014      .65335 
49.747      .69677 

.99970 
.99975 
.99980 

4.70 
4.80 
4.90 

109.95     .04118 
121.51      .08461 
134.29      .12804 

.00910 
.00823 
.00745 

54.969      .74012 
60.751     .78355 
67.141      .82699 

54.978     .74019 
60.759      .78361 
67.149      .82704 

.99983 
.99986 
.99989 

5.00 

148.41      .17147 

.00674 

74.203      .87042 

74.210      .87046 

.99991 

5.10 
5.20 
5.30 

164.02      .21490 
181.27      .25833 
200.34      .30176 

.00610 
.00552 
.00499 

82.008      .91386 
90.633      .95729 
100.17      .00072 

82.014      .91389 
90.639      .95731 
100.17      .00074 

.99993 
.99994 
.99995 

5.40 
5.50 
5.60 

221.41      .34519 
244.69      .38862 
270.43      .43205 

.00452 
.00409 
.00370 

110.70     .04415 
122.34      .08758 
135.21      .13101 

110.71      .04417 
122.35      .08760 
135.22      .13103 

.99996 
.99997 
.99997 

5.70 
5.80 
5.90 

298.87     .47548 
330.30      .51891 
365.04      .56234 

.00335 
.00303 
.00274 

149.43     .17444 
165.15      .21787 
182.52      .26130 

149.44      .17445 
165.15      .21788 
182.52      .26131 

.99998 
.99998 
.99998 

6.00 

403.43     .60577 

.00248 

201.71      .30473 

201.72      .30474 

.99999 

6.25 
6.50 
6.75 

518.01      .71434 
665.14      .82291 
854.06      .93149 

.00193 
.00150 
.00117 

259.01      .41331 
332.57      .52188 
427.03      .63046 

259.01      .41331 
332.57      .52189 
427.03      .63046 

.99999 
1.0000 
1.0000 

7.00 
7.50 
8.00 

1096.6      .04006 
1808.0      .25721 
2981.0     .47436 

.00091 
.00055 
.00034 

548.32     .73903 
904.02      .95618 
1490.5      .17333 

548.32      .73903 
904.02      .95618 
1490.5      .17333 

1.0000 
1.0000 
1.0000 

8.50 
9.00 
9.50 

4914.8     .69150 
8103.1      .90865 
13360.      .12580 

.00020 
.00012 
.00007 

2457.4     .39047 
4051.5      .60762 
6679.9      .82477 

2457.4     .39047 
4051.5      .60762 
6679.9      .82477 

1.0000 
1.0000 
1.0000 

10.00 

22026.      .34294 

.00005 

11013.      .04191 

11013.      .04191 

1.0000 

X]         Table  X  —  Values  and  Logarithms  of  Haversines        123 

[Characteristics  of  Logarithms  omitted — determine  by  rule  from  the  value] 


0 

0' 
Value  Log™ 

10' 
Value  Logio 

20' 
Value  Logio 

30' 
Value  Logio 

40' 
Value  Logio 

50' 
Value  Logio 

0 

.0000 

.00004.3254 

.00004.9275 

.00005.2796 

.00005.5295 

.0001  5.7223 

1 

.00015.8817 

.00016.0156 

.00016.1315 

.0002  .2338 

.0002  .3254 

.0003  .4081 

o 

.0003  .4837 

.0004  .5532 

.0004  .6176 

.0005  .6775 

.0005  .7336 

.0006  .7862 

3 

.0007  .8358 

.0008  .8828 

.0008  .9273 

.0009  .9697 

.0010  .0101 

.0011  .0487 

4 

.0012  .0856 

.0013  .1211 

.0014  .1551 

.0015  .1879 

.0017  .2195 

.0018  .2499 

5 

.0019  .2793 

.0020  .3078 

.0022  .3354 

.0023  .3621 

.0024  .3880 

.0026  .4132 

6 

.0027  .4376 

.0029  .4614 

.0031  .4845 

.0032  .5071 

.0034  .5290 

.0036  .5504 

7 

.0037  .5713 

.0039  .5918 

.0041  .6117 

.0043  .6312 

.0045  .6503 

.0047  .6689 

8 

.0049  .6872 

.0051  .7051 

.0053  .7226 

.0055  .7397 

.0057  .7566 

.0059  .7731 

9 

.0062  .7893 

.0064  .8052 

.0066  .8208 

.0069  .8361 

.0071  .8512 

.0073  .8660 

10 

.0076  .8806 

.0079  .8949 

.0081  .9090 

.0084  .9229 

.0086  .9365 

.0089  .9499 

11 

.0092  .9631 

.0095  .9762 

.0097  .9890 

.0100  .0016 

.0103  .0141 

.0106  .0264 

12 

.0109  .0385 

.0112  .0504 

.0115  .0622 

.0119  .0738 

.0122  .0853 

.0125  .0966 

13 

.0128  .1077 

.0131  .1187 

.0135  .1296 

.0138  .1404 

.0142  .1510 

.0145  .1614 

14 

.0149  .1718 

.0152  .1320 

.0156  .1921 

.0159  .2021 

.0163  .2120 

.0167  .2218 

15 

.0170  .2314 

.0174  .2409 

.0178  .2504 

.0182  .2597 

.0186  .2689 

.0190  .2781 

16 

.0194  .2871 

.0198  .2961 

.0202  .3049 

.0206  .3137 

.0210  .3223 

.0214  .3309 

17 

.0218  .3394 

.0223  .3478 

.0227  .3561 

.0231  .3644 

.0236  .3726 

.0240  .3806 

18 

.0245  .3887 

.0249  .3966 

.0254  .4045 

.0258  .4123 

.0263  .4200 

.0268  .4276 

19 

.0272  .4352 

.0277  .4427 

.0282  .4502 

.0287  .4576 

.0292  .4649 

.0297  .4721 

20 

.0302  .4793 

.0307  .4865 

.0312  .4936 

.0317  .5006 

.0322  .5075 

.0327  .5144 

21 

.0332  .5213 

.0337  .5281 

.0343  .5348 

.0348  .5415 

.0353  .5481 

.0359  .5547 

22 

.0364  .5612 

.0370  .5677 

.0375  .5741 

.0381  .5805 

.0386  .5868 

.0392  .5931 

23 

.0397  .5993 

.0403  .6055 

.0409  .6116 

.0415  .6177 

.0421  .6238 

.0426  .6298 

24 

.0432  .6357 

.0438  .6417 

.0444  .6476 

.0450  .6534 

.0456  .6592 

.0462  .6650 

25 

.0468  .6707 

.0475  .6764 

.0481  .6820 

.0487  .6876 

.0493  .6932 

.0500  .6987 

26 

.0506  .7042 

.0512  .7096 

.0519  .7151 

.0525  .7204 

.0532  .7258 

.0538  .7311 

27 

.0545  .7364 

.0552  .7416 

.0558  .7468 

.0565  .7520 

.0572  .7572 

.0578  .7623 

28 

.0585  .7673 

.0592  .7724 

.0599  .7774 

.0606  .7824 

.0613  .7874 

.0620  .7923 

29 

.0627  .7972 

.0634  .8020 

.0641  .8069 

.0648  .8117 

.0655  .8165 

.0663  .8213 

30 

.0670  .8260 

.0677  .8307 

.0684  .8354 

.0692  .8400 

.0699  .8446 

.0707  .8492 

31 

.0714  .8538 

.0722  .8583 

.0729  .8629 

.0737  .8673 

.0744  .8718 

.0752  .8763 

32 

.0760  .8807 

.0767  .8851 

.0775  .8894 

.0783  .8938 

.0791  .8981 

.0799  .9024 

33 

.0807  .9067 

.0815  .9109 

.0823  .9152 

.0831  .9194 

.0839  .9236 

.0847  .9277 

34 

.0855  .9319 

.0863  .9360 

.0871  .9401 

.0879  .9442 

.0888  .9482 

.0896  .9523 

35 

.0904  .9563 

.0913  .9603 

.0921  .9643 

.0929  .9682 

.0938  .9722 

.0946  .9761 

36 

.0955  .9800 

.0963  .9838 

.0972  .9877 

.0981  .9915 

.0989  .9954 

.0998  .9992 

37 

.1007  .0030 

.1016  .0067 

.1024  .0105 

.1033  .0142 

.1042  .0179 

.1051  .0216 

38 

.1060  .0253 

.1069  .0289 

.1078  .0326 

.1087  .0362 

.1096  .0398 

.1105  .0434 

39 

.1114  .0470 

.1123  .0505 

.1133  .0541 

.1142  .0576 

.1151  .0611 

.1160  .0646 

40 

.1170  .0681 

.1179  .0716 

.1189  .0750 

.1198  .0784 

.1207  .0817 

.1217  .0853 

41 

.1226  .0887 

.1236  .0920 

.1246  .0954 

.1255  .0987 

.1265  .1021 

.1275  .1054 

42 

.1284  .1087 

.1294  .1119 

.1304  .1152 

.1314  .1185 

.1323  .1217 

.1333  .1249 

43 

.1343  .1282 

.1353  .1314 

.1363  .1345 

.1373  .1377 

.1383  .1409 

.1393  .1440 

44 

.1403  .1472 

.1413  .1503 

.1424  .1534 

.1434  .1565 

.1444  .1596 

.1454  .1626 

45 

.1464  .1657 

.1475  .1687 

.1485  .1718 

.1495  .1748 

.1506  .1778 

.1516  .1808 

46 

.1527  .1838 

.1538  .1867 

.1548  .1897 

.1558  .1926 

.1569  .1956 

.1579  .1985 

47 

.1590  .2014 

.1600  .2043 

.1611  .2072 

.1622  .2101 

.1633  .2129 

.1644  .2158 

48 

.1654  .2186 

.1665  .2215 

.1676  .2243 

.1687  .2271 

.1698  .2299 

.1709  .2327 

49 

.1720  .2355 

.1731  .2382 

.1742  .2410 

.1753  .2437 

.1764  .2465 

.1775  .2492 

50 

.1786  .2519 

.1797  .2546 

.1808  .2573 

.1820  .2600 

.1831  .2627 

.1842  .2653 

51 

.1853  .2680 

.1865  .2706 

.1876  .2732 

.1887  .2759 

.1899  .2785 

.1910  .2811 

52 

.1922  .2837 

.1933  .2863 

.1945  .2888 

.1956  .2914 

.1968  .2940 

.1979  .2965 

53 

.1991  .2991 

.2003  .3016 

.2014  .3041 

.2026  .3066 

.2038  .3091 

.2049  .3116 

54 

.2061  .3141 

.2073  .3166 

.2085  .3190 

.2096  .3215 

.2108  .3239 

.2120  .3264 

55 

.2132  .3288 

.2144  .3312 

.2156  .3336 

.2168  .3361 

.2180  .3384 

.2192  .3408 

56 

.2204  .3432 

.2216  .3456 

.2228  .3480 

.2240  .3503 

.2252  .3527 

.2265  .3550 

57 

.2277  .3573 

.2289  .3596 

.2301  .3620 

.2314  .3643 

.2326  .3666 

.2338  .3689 

58 

.2350  .3711 

.2363  .3734 

.2375  .3757 

.2388  .3779 

.2400  .3802 

.2412  .3824 

59 

.2425  .3847 

.2437  .3869 

.2450  .3891 

.2462  .3913 

.2475  .3935 

.2487  .3957 

124  Values  and  Logarithms  of  Haversines 

[Characteristics  of  Logarithms  omitted — determine  by  rule  from  the  value] 


0 

0' 
Value  Logio 

10' 
Value  Logic 

20' 
Value  Logio 

30' 
Value  Logio 

40' 
Value  Logio 

50' 
Value  Logio 

60 

.2500  .3979 

.2513  .4001 

.2525  .4023 

.2538  .4045 

.2551  .4066 

.2563  .4088 

61 

.2576  .4109 

.2589  .4131 

.2601  .4152 

.2614  .4173 

.2627  .4195 

.2640  .4216 

62 

.2653  .4237 

.2665  .4258 

.2678  .4279 

.2691  .4300 

.2704  .4320 

.2717  .4341 

63 

.2730  .4362 

.2743  .4382 

.2756  .4403 

.2769  .4423 

.2782  .4444 

.2795  .4464 

64 

.2808  .4484 

.2821  .4504 

.2834  .4524 

.2847  .4545 

.2861  .4565 

.2874  .4584 

65 

.2887  .4604 

.2900  .4624 

.2913  .4644 

.2927  .4664 

.2940  .4683 

.2953  .4703 

66 

.2966  .4722 

.2980  .4742 

.2993  .4761 

.3006  .4780 

.3020  .4799 

.3033  .4819 

67 

.3046  .4838 

.3060  .4857 

.3073  .4876 

.3087  .4895 

.3100  .4914 

.3113  .4932 

68 

.3127  .4951 

.3140  .4970 

.3154  .4989 

.3167  .5007 

.3181  .5026 

.3195  .5044 

69 

.3208  .5063 

.3222  .5081 

.3235  .5099 

.3249  .5117 

.3263  .5136 

.3276  .5154 

70 

.3290  .5172 

.3304  .5190 

.3317  .5208 

.3331  .5226 

.3345  .5244 

.3358  .5261 

71 

.3372  .5279 

.3386  .5297 

.3400  .5314 

.3413  .5332 

.3427  .5349 

.3441  .5367 

72 

.3455  .5384 

.3469  .5402 

.3483  .5419 

.3496  .5436 

.3510  .5454 

.3524  .5471 

73 

.3538  .5488 

.3552  .5505 

.3566  .5522 

.3580  .5539 

.3594  .5556 

.3608  .5572 

74 

.3622  .5589 

.3636  .5606 

.3650  .5623 

.3664  .5639 

.3678  .5656 

.3692  .5672 

75 

.3706  .5689 

.3720  .5705 

.3734  .5722 

.3748  .5738 

.3762  .5754 

.3776  .5771 

76 

.3790  .5787 

.3805  .5803 

.3819  .5819 

.3833  .5835 

.3847  .5851 

.3861  .5867 

77 

.3875  .5883 

.3889  .5899 

.3904  .5915 

.3918  .5930 

.3932  .5946 

.3946  .5962 

78 

.3960  .5977 

.3975  .5993 

.3989  .6009 

.4003  .6024 

.4017  .6039 

.4032  .6055 

79 

.4046  .6070 

.4060  .6085 

.4075  .6101 

.4089  .6116 

.4103  .6131 

.4117  .6146 

80 

.4132  .6161 

.4146  .6176 

.4160  .6191 

.4175  .6206 

.4189  .6221 

.4203  .6236 

81 

.4218  .6251 

.4232  .6266 

.4247  .6280 

.4261  .6295 

.4275  .6310 

.4290  .6324 

82 

.4304  .6339 

.4319  .6353 

.4333  .6368 

.4347  .6382 

.4362  .6397 

.4376  .6411 

83 

.4391  .6425 

.4405  .6440 

.4420  .6454 

.4434  .6468 

.4448  .6482 

.4463  .6496 

84 

.4477  .6510 

.4492  .6524 

.4506  .6538 

.4521  .6552 

.4535  .6566 

.4550  .6580 

85 

.4564  .6594 

.4579  .6607 

.4593  .6621 

.4608  .6635 

.4622  .6649 

.4637  .6662 

86 

.4651  .6676 

.4666  .6689 

.4680  .6703 

.4695  .6716 

.4709  .6730 

.4724  .6743 

87 

.4738  .6756 

.4753  .6770 

.4767  .6783 

.4782  .6796 

.4796  .6809 

.4811  .6822 

88 

.4826  .6835 

.4840  .6848 

.4855  .6862 

.4869  .6875 

.4884  .6887 

.4898  .6900 

89 

.4913  .6913 

.4937  .6926 

.4942  .6939 

.4956  .6952 

.4971  .6964 

.4985  .6977 

90 

.5000  .6990 

.5015  .7002 

.5029  ."7015 

.5044  .7027 

.5058  .7040 

.5073  .7052 

91 

.5087  .7065 

.5102  .7077 

.5116  .7090 

.5131  .7102 

.5145  .7114 

.5160  .7123 

92 

.5174  .7139 

.5189  .7151 

.5204  .7163 

.5218  .7175 

.5233  .7187 

.5247  .7199 

93 

.5262  .7211 

.5276  .7223 

.5291  .7235 

.5305  .7247 

.5320  .7259 

.5334  .7271 

94 

.5349  .7283 

.5363  .7294 

.5378  .7306 

.5392  .7318 

.5407  .7329 

.5421  .7341 

95 

.5436  .7353 

.5450  .7364 

.5465  .7376 

.5479  .7387 

.5494  .7399 

.5508  .7410 

96 

.5523  .7421 

.5537  .7433 

.5552  .7444 

.5566  .7455 

.5580  .7467 

.5595  .7478 

97 

.5609  .7489 

.5624  .7500 

.5638  .7511 

.5653  .7523 

.5667  .7534 

.5682  .7545 

98 

.5696  .7556 

.5710  .7567 

.5725  .7577 

.5739  .7588 

.5753  .7599 

.5768  .7610 

99 

.5782  .7621 

.5797  .7632 

.5811  .7642 

.5825  .7653 

.5840  .7664 

.5854  .7674 

100 

.5868  .7685 

.5883  .7696 

.5897  .7706 

.5911  .7717 

.5925  .7727 

.5940  .7738 

101 

.5954  .7748 

.5968  .7759 

.5983  .7709 

.5997  .7779 

.6011  .7790 

.6025  .7800 

102 

.6040  .7810 

.6054  .7820 

.6068  .7830 

.6082  .7841 

.6096  .7851 

.6111  .7861 

103 

.6125  .7871 

.6139  .7881 

.6153  .7891 

.6167  .7901 

.6181  .7911 

.6195  .7921 

104 

.6210  .7931 

.6224  .7940 

.6238  .7950 

.6252  .7960 

.6266  .7970 

.6280  .7980 

105 

.6294  .7989 

.6308  .7999 

.6322  .8009 

.6336  .8018 

.6350  .8028 

.6364  .8037 

106 

.6378  .8047 

.6392  .8056 

.6406  .8066 

.6420  .8075 

.6434  .8085 

.6448  .8094 

107 

.6462  .8104 

.6476  .8113 

.6490  .8122 

.6504  .8131 

.6517  .8141 

.6531  .8150 

108 

.6545  .8159 

.6559  .8168 

.6573  .8177 

.6587  .8187 

.6600  .8196 

.6614  .8205 

109 

.6628  .8214 

.6642  .8223 

.6655  .8232 

.6669  .8241 

.6683  .8250 

.6696  .8258 

110 

.6710  .8267 

.6724  .8276 

.6737  .8285 

.6751  .8294 

.6765  .8302 

.6778  .8311 

111 

.6792  .8320 

.6805  .8329 

.6819  .8337 

.6833  .8346 

.6846  .8354 

.6860  .8363 

112 

.6873  .8371 

.6887  .8380 

.6900  .8388 

.6913  .8397 

.6927  .8405 

.6940  .8414 

113 

.6954  .8422 

.6967  .8430 

.6980  .8439 

.6994  .8447 

.7007  .8455 

.7020  .8464 

114 

.7034  .8472 

.7047  .8480 

.7060  .8488 

.7073  .8496 

.7087  .8504 

.7100  .8513 

115 

.7113  .8521 

.7126  .8529 

.7139  .8537 

.7153  .8545 

.7166  .8553 

.7179  .8561 

116 

.7192  .8568 

.7205  .8576 

.7218  .8584 

.7231  .8592 

.7244  .8600 

.7257  .8608 

117 

.7270  .8615 

.7283  .8623 

.7296  .8631 

.7309  .8638 

.7322  .8646 

.7335  .8654 

118 

.7347  .8661 

.7360  .8669 

.7373  .8676 

.7386  .8684 

.7399  .8691 

.7411  .8699 

119 

.7424  .8706 

.7437  .8714 

.7449  .8721 

.7462  .8729 

.7475  .8736 

.7487  .8743 

X]  Values  and  Logarithms  of  Haversines 

[Characteristics  of  Logarithms  omitted — determine  by  rule  from  the  value] 


125 


o 

0' 
Value  Logic 

10' 
Value  Logio 

20' 
Value  Logio 

30' 
Value  Logic 

40' 
Value  Logio 

50' 

Value  Logio 

120 

.7500  .8751 

.7513  .8758 

.7525  .8765 

.7538  .8772 

.7550  .8780 

.7563  .8787 

121 

.7575  .8794 

.7588  .8801 

.7600  .8808 

.7612  .8815 

.7625  .8822 

.7637  .8829 

122 

.7650  .8836 

.7662  .8843 

.7674  .8850 

.7686  .8857 

.7699  .8864 

.7711  .8871 

123 

.7723  .8878 

.7735  .8885 

.7748  .8892 

.7760  .8898 

.7772  .8905 

.7784  .8912 

124 

.7796  .8919 

.7808  .8925 

.7820  .8932 

.7832  .8939 

.7844  .8945 

.7856  .8952 

125 

.7868  .8959 

.7880  .8965 

.7892  .8972 

.7904  .8978 

.7915  .8985 

.7927  .8991 

126 

.7939  .8998 

.7951  .9004 

.7962  .9010 

.7974  .9017 

.7986  .9023 

.7997  .9030 

127 

.8009  .9036 

.8021  .9042 

.8032  .9048 

.8044  .9055 

.8055  .9061 

.8067  .9067 

128 

.8078  .9073 

.8090  .9079 

.8101  .9085 

.8113  .9092 

.8124  .9098 

.8135  .9104 

129 

.8147  .9110 

.8158  .9116 

.8169  .9122 

.8180  .9128 

.8192  .9134 

.8203  .9140 

130 

.8214  .9146 

.8225  .9151 

.8236  .9157 

.8247  .9163 

.8258  .9169 

.8269  .9175 

131 

.8280  .9180 

.8291  .9186 

.8302  .9192 

.8313  .9198 

.8324  .9203 

.8335  .9209 

132 

.8346  .9215 

.8356  .9220 

.8367  .9226 

.8378  .9231 

.8389  .9237 

.8399  .9242 

133 

.8410  .9248 

.8421  .9253 

.8431  .9259 

.8442  .9264 

.8452  .9270 

.8463  .9275 

134 

.8473  .9281 

.8484  .9286 

.8494  .9291 

.8501  .9297 

.8515  .9302 

.8525  .9307 

135 

.8536  .9312 

.8546  .9318 

.8556  .9323 

.8566  .9328 

.8576  .9333 

.8587  .9338 

136 

.8597  .9343 

.8607  .9348 

.8617  .9353 

.8627  .9359 

.8637  .9364 

.8647  .9369 

137 

.8657  .9374 

.8667  .9379 

.8677  .9383 

.8686  .9388 

.8696  .9393 

.8706  .9398 

138 

.8716  .9403 

.8725  .9408 

.8735  .9413 

.8745  .9417 

.8754  .9422 

.8764  .9427 

139 

.8774  .9432 

.8783  .9436 

.8793  .9441 

.8802  .9446 

.8811  .9450 

.8821  .9455 

140 

.8830  .9460 

.8840  .9464 

.8849  .9469 

.8858  .9473 

.8867  .9478 

.8877  .9482 

141 

.8886  .9487 

.8895  .9491 

.8904  .9496 

.8913  .9500 

.8922  .9505 

.8931  .9509 

142 

.8940  .9513 

.8949  .9518 

.8958  .9522 

.8967  .9526 

.8976  .9531 

.8984  .9535 

143 

.8993  .9539 

.9002  .9543 

.9011  .9548 

.9019  .9552 

.9028  .9556 

.9037  .9560 

144 

.9045  .9564 

.9054  .9568 

.9062  .9572 

.9071  .9576 

.9079  .9580 

.9087  .9584 

145 

.9096  .9588 

.9104  .9592 

.9112  .9596 

.9121  .9600 

.9129  .9604 

.9137  .9608 

146 

.9145  .9612 

.9153  .9616 

.9161  .9620 

.9169  .9623 

.9177  .9627 

.9185  .9631 

147 

.9193  .9635 

.9201  .9638 

.9209  .9642 

.9217  .9646 

.9225  .9650 

.9233  .9653 

148 

.9240  .9657 

.9248  .9660 

.9256  .9664 

.9263  .9668 

.9271  .9671 

.9278  .9675 

149 

.9286  .9678 

.9293  .9682 

.9301  .9685 

.9308  .9689 

.9316  .9692 

.9323  .9695 

150 

.9330  .9699 

.9337  .9702 

.9345  .9706 

.9352  .9709 

.9359  .9712 

.9366  .9716 

151 

.9373  .9719 

.9380  .9722 

.9387  .9725 

.9394  .9729 

.9401  .9732 

.9408  .9735 

152 

.9415  .9738 

.9422  .9741 

.9428  .9744 

.9435  .9747 

.9442  .9751 

.9448  .9754 

153 

.9455  .9757 

.9462  .9760 

.9468  .9763 

.9475  .9766 

.9481  .9769 

.9488  .9772 

154 

.9494  .9774 

.9500  .9777 

.9507  .9780 

.9513  .9783 

.9519  .9786 

.9525  .9789 

155 

.9532  .9792 

.9538  .9794 

.9544  .9797 

.9550  .9800 

.9556  .9803 

.9562  .9805 

156 

.9568  .9808 

.9574  .9811 

.9579  .9813 

.9585  .9816 

.9591  .9819 

.9597  .9821 

157 

.9603  .9824 

.9608  .9826 

.9614  .9829 

.9619  .9831 

.9625  .9834 

.9630  .9836 

158 

.9636  .9839 

.9641  .9841 

.9647  .9844 

.9652  .9846 

.9657  .9849 

.9663  .9851 

159 

.9668  .9853 

.9673  .9856 

.9678  .9858 

.9683  .9860 

.9688  .9863 

.9693  .9865 

160 

.9698  .9867 

.9703  .9869 

.9708  .9871 

.9713  .9874 

.9718  .9876 

.9723  .9878 

161 

.9728  .9880 

.9732  .9882 

.9737  .9884 

.9742  .9886 

.9746  .9888 

.9751  .9890 

162 

.9755  .9892 

.9760  .9894 

.9764  .9896 

.9769  .9898 

.9773  .9900 

.9777  .9902 

163 

.9782  .9904 

.9786  .9906 

.9790  .9908 

.9794  .9910 

.9798  .9911 

.9802  .9913 

164 

.9806  .9915 

.9810  .9917 

.9814  .9919 

.9818  .9920 

.9822  .9922 

.9826  .9923 

165 

.9830  .9925 

.9833  .9927 

.9837  .9929 

.9841  .9930 

.9844  .9932 

.9848  .9933 

166 

.9851  .9935 

.9855  .9937 

.9858  .9938 

.9862  .9940 

.9865  .9941 

.9869  .9943 

167 

.9872  .9944 

.9875  .9945 

.9878  .9947 

.9881  .9948 

.9885  .9950 

.9888  .9951 

168 

.9891  .9952 

.9894  .9954 

.9897  .9955 

.9900  .9956 

.9903  .9957 

.9905  .9959 

169 

.9908  .9960 

.9911  .9961 

.9914  .9962 

.9916  .9963 

.9919  .9965 

.9921  .9966 

170 

.9924  .9967 

.9927  .9968 

.9929  .9969 

.9931  .9970 

.9934  .9971 

.9936  .9972 

171 

.9938  .9973 

.9941  .9974 

.9943  .9975 

.9945  .9976 

.9947  .9977 

.9949  .9978 

172 

.9951  .9979 

.9953  .9980 

.9955  .9981 

.9957  .9981 

.9959  .9982 

.9961  .9983 

173 

.9963  .9984 

.9964  .9984 

.9966  .9985 

.9968  .9986 

.9969  .9987 

.9971  .9987 

174 

.9973  .9988 

.9974  .9988 

.9976  .9989 

.9977  .9990 

.9978  .9991 

.9980  .9991 

175 

.9981  .9992 

.9982  .9992 

.9983  .9993 

.9985  .9993 

.9986  .9994 

.9987  .9994 

176 

.9988  .9995 

.9989  .9995 

.9990  .9996 

.9991  .9996 

.9992  .9996 

.9992  .9997 

177 

.9993  .9997 

.9994  .9997 

.9995  .9998 

.9995  .9998 

.9996  .9998 

.9996  .9998 

178 

.9997  .9999 

.9997  .9999 

.9998  .9999 

.9998  .9999 

.9999  .9999 

.9999  .9999 

179 

.9999  .9999 

.9999  .9999 

.9999  .9999 

.9999  .9999 

.9999  .0000 

1.0000  .0000 

126      Table  XI  —  Factor  Table  —  Logarithms  of  Primes       [XI 

[If  N  is  prime,  Its  logarithm  Is  given.    If  N  Is  not  prime,  Its  factors  are  given.] 


N 

1 

3 

7 

9 

N 

LogN 

10 

0043213738 

0128372247 

0293837777 

0374264979 

2 

301029995004 

11 

3-37 

0530784435 

32-13 

7-17 

3 

477121254720 

12 

II2 

3-41 

1038037210 

3-43 

5 

698970004336 

13 

1172712957 

7-19 

1367205672 

1430148003 

7 

845098040014 

14 

3-47 

11-13 

3-72 

1731862684 

11 

041392685158 

15 

1789769473 

32-17 

1958996524 

3-53 

13 

113943352307 

16 

7-23 

2121876044 

2227164711 

132 

17 

230448921378 

17 

32-19 

2380461031 

3-59 

2528530310 

19 

278753600953 

18 

2576785749 

3-61 

11-17 

33-7 

23 

361727836018 

19 

2810333672 

2855573090 

2944662262 

2988530764 

29 

462397997899 

20 

3-67 

7-29 

32-23 

11-19 

31 

491361693834 

21 

3242824553 

3-71 

7-31 

3-73 

37 

568201724067 

22 

13-17 

3483048630 

3560258572 

3598354823 

41 

612783856720 

23 

3-7-11 

3673559210 

3-79 

3783979009 

43 

633468455580 

24 

3820170426 

35 

13-19 

3-83 

47 

672097857936 

25 

3996737215 

11-23 

4099331233 

7-37 

53 

724275869601 

26 

32-29 

4199557485 

3-89 

4297522800 

59 

770852011642 

27 

4329692909 

3-7-13 

4424797691 

32-31 

61 

785329835011 

28 

4487063199 

4517864355 

7-41 

172 

67 

826074802701 

29 

3-97 

4668676204 

33-ll 

13-23 

71 

851258348719 

30 

7-43 

3-101 

4871383755 

3-103 

73 

863322860120 

31 

4927603890 

4955443375 

5010592622 

11-29 

79 

897627091290 

32 

3-107 

17-19 

3-109 

7-47 

83 

919078092376 

33 

5198279938 

32-37 

5276299009 

3-113 

89 

949390006645 

34 

11-31 

73 

5403294748 

5428254270 

97 

986771734266 

35 

3'-13 

5477747054 

3-7-17 

5550944486 

1301 

1142772966 

36 

192 

3-112 

5646660643 

32-41 

1303 

1149444157 

37 

7-53 

5717088318 

13-29 

5786392100 

1307 

1162755876 

38 

3-127 

5831987740 

32-43 

5899496013 

1319 

1202447955 

39 

17-23 

3-131 

5987905068 

3-7-19 

1321 

1209028176 

40 

6031443726 

13-31 

11-37 

6117233080 

1327 

1228709229 

41 

3-137 

7-59 

3-139 

6222140230 

1361 

1338581252 

42 

6242820958 

32-47 

7-61 

3-11-13 

1367 

1357685146 

43 

6344772702 

6364878964 

19-23 

6424645202 

1373 

1376705372 

44 

32.72 

6464037262 

3-149 

6522463410 

1381 

1401936786 

45 

11-41 

3-151 

6599162001 

3'-  17 

1399 

1458177145 

46 

6637009254 

6655809910 

6693168806 

7-67 

1409 

1489109931 

47 

3-157 

11-43 

32-53 

6803355134 

1423 

1532049001 

48 

13-37 

3-7-23 

6875289612 

3-163 

1427 

1544239731 

49 

6910814921 

17-29 

7-71 

6981005456 

1429 

1550322288 

50 

3-167 

7015679851 

3-132 

7067177823 

1433 

1562461904 

51 

7-73 

33-19 

11-47 

3-173 

1439 

1580607939 

52 

7168377233 

7185016889 

17-31 

232 

1447 

1604685311 

53 

32-59 

13-41 

3-179 

72-ll 

1451 

1616674124 

54 

7331972651 

3-181 

7379873263 

32-61 

1453 

1622656143 

55 

19-29 

7-79 

7458551952 

13-43 

1459 

1640552919 

56 

3-11-17 

7505083949 

3<-7 

7551122664 

1471 

1676126727 

57 

7566361082 

3-191 

7611758132 

3-193 

1481 

1705550585 

58 

7-83 

11-53 

7686381012 

19-31 

1483 

1711411510 

59 

3-197 

7730546934 

3-199 

7774268224 

1487 

1723109685 

60 

7788744720 

32-67 

7831886911 

3-7-29 

1489 

1728946978 

61 

13-47 

7874604745 

7902851640 

7916906490 

1493 

1740598077 

62 

33-23 

7-89 

3-11-19 

17-37 

1499 

1758016328 

63 

8000293592 

3-211 

72-13 

32-71 

1511 

1792644643 

64 

8068580295 

8082109729 

8109042807 

11-59 

1523 

1826999033 

65 

3-7-31 

8149131813 

32-73 

8188854146 

1531 

1849751907 

66 

8202014595 

3-13-17 

23-29 

3-223 

1543 

1883659261 

67 

11-61 

8280150642 

8305886687 

7-97 

1549 

1900514178 

68 

3-227 

8344207037 

3-229 

13-53 

1553 

1911714557 

69 

8394780474 

32-7-ll 

17-41 

3-233 

1559 

1928461152 

XI J  Factor  Table  —  Logarithms  of  Primes 

[If  N  Is  a  prime,  Its  logarithm  is  given.    If  N  is  not  a  prime,  Ita  factors  are  given,] 


127 


N 

1 

3 

7 

9 

N 

LogN 

70 

8457180180 

19-37 

7-101 

8506462352 

1567 

1950689965 

71 

32-79 

23-31 

3-239 

8567288904 

1571 

1961761850 

72 

7-103 

3-241 

8615344109 

3« 

1579 

1983821300 

73 

17-43 

8651039746 

11-67 

8686444384 

1583 

1994809149 

74 

3-13-19 

8709888138 

32-83 

7-107 

1597 

2033049161 

75 

8756399370 

3-251 

8790958795 

3-11-23 

1601 

2043913319 

76 

8813846568 

7-109 

13-59 

8859263398 

1607 

2060158768 

77 

3-257 

8881794939 

3-7-37 

19-41 

1609 

2065560441 

78 

11-71 

33-29 

8959747324 

3-263 

1613 

2076343674 

79 

7-113 

13-61 

9014583214 

17-47 

1619 

2092468488 

80 

32-89 

11-73 

3-269 

9079485216 

1621 

2097830148 

81 

9090208542 

3-271 

19-43 

32-7-13 

1627 

2113875529 

82 

9143431571 

9153998352 

9175055096 

9185545306 

1637 

2140486794 

83 

3-277 

72.17 

33-31 

9237619608 

1657 

2193225084 

84 

29" 

3-281 

7-112 

3-283 

1663 

2208922492 

85 

23-37 

9309490312 

9329808219 

9339931638 

1667 

2219355998 

86 

3-7-41 

9360107957 

3-172 

11-79 

1669 

2224563367 

87 

13-67 

32-97 

9429995934 

3-293 

1693 

2286569581 

88 

9449759084 

9459607036 

9479236198 

7-127 

1697 

2296818423 

89 

3<-ll 

19-47 

3-13-23 

29-31 

1699 

2301933789 

90 

17-53 

3-7-43 

9576072871 

32-101 

1709 

2327420627 

91 

9595183770 

11-83 

7-131 

9633155114 

1721 

2357808703 

92 

3-307 

13-71 

32-103 

9680157140 

1723 

2362852774 

93 

72-19 

3-311 

9717395909 

3-313 

1733 

2387985627 

94 

9735896234 

23-41 

9763499790 

13-73 

1741 

2407987711 

95 

3-317 

9790929006 

3'll-29 

7-137 

1747 

2422929050 

96 

312 

32-107 

9854264741 

3-17-19 

1753 

2437819161 

97 

9872192299 

7-139 

9898945637 

11-89 

1759 

2452658395 

98 

32-109 

9925535178 

3-7-47 

23-43 

1777 

2496874278 

99 

9960736545 

3-331 

9986951583 

33-37 

1783 

2511513432 

100 

7-11-13 

17-59 

19-53 

0038911662 

1787 

2521245525 

101 

3-337 

0056094454 

32-113 

0081741840 

1789 

2526103406 

102 

0090257421 

3-11-31 

13-79 

3-73 

1801 

2555137128 

103 

0132586653 

0141003215 

17-61 

0166155476 

1811 

2579184503 

104 

3-347 

7-149 

3-349 

0207754882 

1823 

2607866687 

105 

0216027160 

34-13 

7-1C1 

3-353 

1831 

2626883443 

106 

0257153839 

0265332645 

11-97 

0289777052 

1847 

2664668954 

107 

32-7-17 

29-37 

3-359 

13-83 

1861 

2697463731 

108 

23-47 

3-192 

0362295441 

S2-!!* 

1867 

2711443179 

109 

0378247506 

0386201619 

0402066276 

7-157 

1871 

2720737875 

110 

3-367 

0425755124 

3"-41 

0449315461 

1873 

2725377774 

111 

11-101 

3-7-53 

0480531731 

3-373 

1877 

2734642726 

112 

19-59 

0503797563 

72-23 

0526939419 

1879 

2739267801 

113 

3-13-29 

11-103 

3-379 

17-67 

1889 

2762319579 

114 

7-163 

32-127 

31-37 

3-383 

1901 

2789821169 

115 

0610753236 

0618293073 

13-89 

19-61 

1907 

2803506930 

116 

33-43 

0655797147 

3-389 

7-167 

1913 

2817149700 

117 

0685568951 

3-17-23 

11-107 

32-131 

1931 

2857822738 

118 

0722498976 

7-132 

0744507190 

29-41 

1933 

2862318540 

119 

3-397 

0766404437 

32-7-19 

11-109 

1949 

2898118391 

120 

0795430074 

3-401 

17-71 

3-13-31 

1951 

2902572694 

121 

7-173 

0838608009 

0852905782 

23-53 

1973 

2961270853 

122 

3-11-37 

0874264570 

3-409 

0895518829 

1979 

2964457942 

123 

0902580529 

32-137 

0923696996 

3-7-59 

1987 

2981978671 

124 

17-73 

11-113 

29-43 

0965624384 

1993 

2995072987 

125 

32-139 

7-179 

3-419 

1000257301 

1997 

3003780649 

126 

13-97 

3-421 

7-181 

33-47 

1999 

3008127941 

127 

31-41 

19-67 

1061908973 

1068705445 

2003 

3016809493 

128 

3-7  61 

1082266564 

32-ll-13 

1102529174 

2011 

3034120706 

129 

1109262423 

3-431 

1129399761 

3-433 

2017 

3047058982 

128  Table  XII  a  —  Compound  Interest:  (1  +  r)n 

AMOUNT  OF  ONE  DOLLAR  PRINCIPAL  AT  COMPOUND  INTEREST  AFTER  n  YEARS 


[XII 


n 

2% 

21  Of 
2  % 

3  erf 
/o 

3i% 

4% 

4\% 

5% 

6% 

7% 

I 
2 
3 

1.0200 
1.0404 
1.0612 

1.0250 
1.0506 
1.0769 

1.0300 
1.0609 
1.0927 

1.0350 
1.0712 
1.1087 

1.0400 
1.0816 
1.1249 

1.0450 
1.0920 
1.1412 

1.0500 
1.1025 
1.1576 

1.0600 
1.1236 
1.1910 

1.0700 
1.1449 
1.2250 

4 
5 
6 

1.0824 
1.1041 
1.1262 

1.1038 
1.1314 
1.1597 

1.1255 
1.1593 
1.1941 

1.1475 
1.1877 
1.2293 

1.1699 
1.2167 
1.2653 

1.1925 
1.2462 
1.3023 

1.2155 
1.2763 
1.3401 

1.2625 
1.3382 
1.4185 

1.3108 
1.4026 
1.5007 

7 
8 
9 

1.1487 
1.1717 
1.1951 

1.1887 
1.2184 
1.2489 

1.2299 
1.2668 
1.3048 

1.2723 
1.3168 
1.3629 

1.3159 
1.3686 
1.4233 

1.3609 
1.4221 
1.4861 

1.4071 
1.4775 
1.5513 

1.5036 
1.5938 
1.6895 

1.6058 
1.7182 
1.8385 

10 

1.2190 

1.2801 

1.3439 

1.4106 

1.4802 

1.5530 

1.6289 

1.7908 

1,9672 

11 

12 
13 

1.2434 
1.2682 
1.2936 

1.3121 
1.3449 
1.3785 

1.3842 

1.4258 
1.4685 

1.4600 
1.5111 
1.5640 

1.5395 
1.6010 
1.6651 

1.6229 
1.6959 

1.7722 

1.7103 
1.7959 
1.8856 

1.8983 
2.0122 
2.1329 

2.1049 
2.2522 
2.4098 

14 
15 
16 

1.3195 
1.3459 
1.3728 

1.4130 
1.4483 
1.4845 

1.5126 
1.5580 
1.6047 

1.6187 
1.6753 
1.7340 

1.7317 
1.8009 
1.8730 

1.8519 
1.9353 
2.0224 

1.9799 

2.0789 
2.1829 

2.2609 
2.3966 
2.5404 

2.5785 
2.7590 
2.9522 

17 
18 
19 

1.4002 
1.4282 
1.4568 

1.5216 
1.5597 
1.5987 

1.6528 
1.7024 
1.7535 

1.7947 
1.8575 
1.9225 

1.9479 

2.0258 
2.1068 

2.1134 
2.2085 
2.3079 

2.2920 
2.4066 
2.5270 

2.6928 
2.8543 
3.0256 

3.1588 
3.3799 
3.6165 

20 

1.4859 

1.6386 

1.8061 

1.9898 

2.1911 

2.4117 

2.6533 

3.2071 

3.8697 

21 
22 
23 

1.5157 
1.5460 
1.5769 

1.6796 
1.7216 
1.7646 

1.8603 
1.9161 
1.9736 

2.0594 
2.1315 
2.2061 

2.2788 
2.3699 
2.4647 

2.5202 
2.6337 
2.7522 

2.7860 
2.9253 
3.0715 

3.3996 
3.6035 
3.8197 

4.1406 
4.4304 
4.7405 

24 
25 
26 

1.6084 
1.6406 
1.6734 

1.8087 
1.8539 
1.9003 

2.0328 
2.0938 
2.1566 

2.2833 
2.3632 
2.4460 

2.5633 
2.6658 
2.7725 

2.8760 
3.0054 
3.1407 

3.2251 
3.3864 
3.5557 

4.0489 
4.2919 

4.5494 

5.0724 
5.4274 
5.8074 

27 

28 
29 

1.7069 
1.7410 
1.7758 

1.9478 
1.9965 
2.0464 

2.2213 
2.2879 
2.3566 

2.5316 
2.6202 
2.7119 

2.8834 
2.9987 
3.1187 

3.2820 
3.4297 
3.5840 

3.7335 
3.9201 
4.1161 

4.8223 
5.1117 
5.4184 

6.2139 
6.6488 
7.1143 

30 

1.8114 

2.0976 

2.4273 

2.8068 

3.2434 

3.7453 

4.3219 

5.7435 

7.6123 

31 
32 
33 

1.8476 
1.8845 
1.9222 

2.1500 
2.2038 
2.2589 

2.5001 
2.5751 
2.6523 

2.9050 
3.0067 
3.1119 

3.3731 
3.5081 
3.6484 

3.9139 
4.0900 
4.2740 

4.5380 
4.7649 
5.0032 

6.0881 
6.4534 
6.8406 

8.1451 
8.7153 
9.3253 

34 
35 
36 

1.9607 
1.9999 
2.0399 

2.3153 
2.3732 
2.4325 

2.7319 
2.8139 
2.8983 

3.2209 
3.3336 
3.4503 

3.7943 
3.9461 
4.1039 

4.4664 
4.6673 

4.8774 

5.2533 
5.5160 
5.7918 

7.2510 
7.6861 
8.1473 

9.9781 
10.6766 
11.4239 

37 
38 
39 

2.0807 
2.1223 
2.1647 

2.4933 
2.5557 
2.6196 

2.9852 
3.0748 
3.1670 

3.5710 
3.6960 
3.8254 

4.2681 
4.4388 
4.6164 

5.0969 
5.3262 
5.5659 

6.0814 
6.3855 

6.7048 

8.6361 
9.1543 
9.7035 

12.2236 
13.0793 
13.9948 

40 

2.2080 

2.6851 

3.2620 

3.9593 

4.8010 

5.8164 

7.0400 

10.2857 

14.9745 

41 
42 
43 

2.2522 
2.2972 
2.3432 

2.7522 
2.8210 
2.8915 

3.3599 
3.4607 
3.5645 

4.0978 
4.2413 
4.3897 

4.9931 
5.1928 
5.4005 

6.0781 
6.3516 
6.6374 

7.3920 
7.7616 
8.1497 

10.9029 
11.5570 
12.2505 

16.0227 
17.1443 
18.3444 

44 
45 
46 

2.3901 
2.4379 
2.4866 

2.9638 
3.0379 
3.1139 

3.6715 
3.7816 
3.8950 

4.5433 

4.7024 
4.8669 

5.6165 
5.8412 
6.0748 

6.9361 

7.2482 
7.5744 

8.5572 
8.9850 
9.4343 

12.9855 
13.7646 
14.5905 

19.6285 
21.0025 
22.4726 

47 
48 
49 

2.5363 

2.5871 
2.6388 

3.1917 
3.2715 
3.3533 

4.0119 
4.1323 
4.2562 

5.0373 
5.2136 
5.3961 

6.3178 
6.5705 
6.8333 

7.9153 

8.2715 
8.6437 

9.9060 
10.4013 
10.9213 

15.4659 
16.3939 
17.3775 

24.0457 
25.7289 
27.5299 

50 

2.6916 

3.4371 

4.3839 

5.5849 

7.1067 

9.0326 

11.4674 

18.4202 

29.4570 

XII  b]     Table  XII  b  —  Compound  Discount:  1/(1  +  r)re 

PRESENT  VALUE  OF  ONE  DOLLAR  DUE  AT  THE  END  OF  n  YEARS 


129 


n 

2% 

2\% 

3% 

3\% 

4% 

4\% 

5% 

6% 

7% 

1 
2 
3 

.98039 
.96117 
.94232 

.97561 
.95181 
.92860 

.97087 
.94260 
.91514 

.96618 
.93351 
.90194 

.96154 
.92456 
.88900 

.95694 
.91573 
.87630 

.95238 
.90703 
.86384 

.94340 
.89000 
.83962 

.93458 
.87344 
.81630 

4 
5 
6 

.92385 
.90573 

.88797 

.90595 
.88385 
.86230 

.88849 
.86261 

.83748 

.87144 
.84197 
.81350 

.85480 
.82193 
.79031 

.83856 
.80245 
.76790 

.82270 
.78353 
.74622 

.79209 
.74726 
.70496 

.76290 
.71299 
.66634 

7 
8 
9 

.87056 
.85349 
.83676 

.84127 
.82075 
.80073 

.81309 
.78941 
.76642 

.78599 
.75941 
.73373 

.75992 
.73069 
.70259 

.73483 
.70319 
.67290 

.71068 
.67684 
.64461 

.66506 
.62741 
.59190 

.62275 
.58201 
.54393 

10 

.82035 

.78120 

.74409 

.70892 

.67556 

.64393 

.61391 

.55839 

.50835 

11 
12 
13 

.80426 
.78849 
.77303 

.76214 
.74356 
.72542 

.72242 
.70138 
.68095 

.68495 
.66178 
.63940 

.64958 
.62460 
.60057 

.61620 
.58966 
.56427 

.58468 
.55684 
.53032 

.52679 
.49697 
.46884 

.47509 
.44401 
.41496 

14 
15 
16 

.75788 
.74301 
.72845 

.70773 
.69047 
.67362 

.66112 
.64186 
.62317 

.61778 
.59689 
.57671 

.57748 
.55526 
.53391 

.53997 
.51672 
.49447 

.50507 
.48102 
.45811 

.44230 
.41727 
.39365 

.38782 
.36245 
.33873 

17 
18 
19 

.71416 
.70016 

.68043 

.65720 
.64117 
.62553 

.60502 
.58739 
.57029 

.55720 
.53836 
.52016 

.51337 
.49363 

.47464 

.47318 
.45280 
.43330 

.43630 
.41552 
.39573 

.37136 
.35034 
.33051 

.31657 
.29586 
.27651 

20 

.67297 

.61027 

.55368 

.50257 

.45639 

.41464 

.37689 

.31180 

.25842 

21 
22 
23 

.65978 
.64684 
.63416 

.59539 
.58086 
.56670 

.53755 
.52189 
.50669 

.48557 
.46915 
.45329 

.43883 
.42196 
.40573 

.39679 
.37970 
.36335 

.35894 
.34185 
.32557 

.29416 
.27751 
.26180 

.24151 
.22571 
.21095 

24 
25 
26 

,62172 
.60953 
.59758 

.55288 
.53939 
.52623 

.49193 
.47761 
.46369 

.43796 
.42315 

.40884 

.39012 
.37512 
.36069 

.34770 
.33273 
.31840 

.31007 
.29530 
.28124 

.24698 
.23300 
.21981 

.19715 
.18425 
.17220 

27 
28 
29 

.58586 
.57437 
.56311 

.51340 
.50088 
.48866 

.45019 
.43708 
.42435 

.39501 
.38165 
.36875 

.34682 
.33348 
.32065 

.30469 
.29157 
.27902 

.26785 
.25509 
.24295 

.20737 
.19563 
.18456 

.16093 
.15040 
.14056 

30 

.55207 

.47674 

.41199 

.35628 

.30832 

.26700 

.23138 

.17411 

.13137 

31 
32 
33 

.54125 
.53063 
.52023 

.46511 
.45377 
.44270 

.39999 
.38834 
.37703 

.34423 
.33259 
.32134 

.29646 
.28506 
.27409 

.25550 
.24450 
.23397 

.22036 
.20987 
.19987 

.16425 
.15496 
.14619 

.12277 
.11474 
.10723 

34 
35 
36 

.51003 
.50003 
.49022 

.43191 
.42137 
.41109 

.36604 
.35538 
.34503 

.31048 
.29998 
.28983 

.26355 
.25342 
.24367 

.22390 
.21425 
.20503 

.19035 
.18129 
.17266 

.13791 
.13011 
.12274 

.10022 
.09366 
.08754 

37 
38 
39 

.48061 
.47119 
.46195 

.40107 
.39128 
.38174 

.33498 
.32523 
.31575 

.28003 
.27056 
.26141 

.23430 
.22529 
.21662 

.19620 
.18775 
.17967 

.16444 
.15661 
.14915 

.11580 
.10924 
.10306 

.08181 
.07646 
.07146 

40 

.45289 

.37243 

.30656 

.25257 

.20829 

.17193 

.14205 

.09722 

.06678 

41 
42 
43 

.44401 
.43530 
.42677 

.36335 
.35448 
.34584 

.29763 
.28896 
.28054 

.24403 
.23578 
.22781 

.20028 
.19257 
.18517 

.16453 
.15744 
.15066 

.13528 
.12884 
.12270 

.09172 
.08653 
.08163 

.06241 
.05833 
.05451 

44 
45 
46 

.41840 
.41020 
.40215 

.33740 
.32917 
.32115 

.27237 
.26444 
.25674 

.22010 
.21266 
.20547 

.17805 
.17120 
.16461 

.14417 
.13796 
.13202 

.11686 
.11130 
.10600 

.07701 
.07265 
.06854 

.05095 
.04761 
.04450 

47 
48 
49 

.39427 
.38654 
.37896 

.31331 
.30567 

.29822 

.24926 
.24200 
.23495 

.19852 
.19181 
.18532 

.15828 
.15219 
.14634 

.12634 
.12090 
.11569 

.10095 
.09614 
.09156 

.06466 
.06100 
.05755 

.04159 
.03887 
.03632 

50 

.37153 

.29094 

.22811 

.17905 

.14071 

.11071 

.08720 

.05429 

.03395 

130 


Table  XII  c  —  Amount  of  an  Annuity 

AMOUNT  OF  AN  ANNUITY  OP  ONE  DOLLAR  PER  YEAR  AFTER  n  YEARS 


[XII  c 


n 

2% 

2\% 

3% 

3i% 

4% 

4k  % 

5% 

6% 

7% 

1 
2 
3 

1.0000 
2.0200 
3.0604 

1.0000 
2.0250 
3.0756 

1.0000 
2.0300 
3.0909 

1.0000 
2.0350 
3.1062 

1.0000 
2.0400 
3.1216 

1.0000 
2.0450 
3.1370 

1.0000 
2.0500 
3.1525 

1.0000 
2.0600 
3.1836 

1.0000 
2.0700 
3.2149 

4 
5 
6 

4.1216 
5.2040 
6.3081 

4.1525 
5.2563 
6.3877 

4.1836 
5.3091 
6.4684 

4.2149 
5.3625 
6.5502 

4.2465 
5.4163 
6.6330 

4.2782 
5.4707 
6.7169 

4.3101 
5.5256 
6.8019 

4.3746 
5.6371 
6.9753 

4.4399 
5.7507 
7.1533 

7 
8 
9 

7.4343 
8.5830 
9.7546 

7.5474 
8.7361 
9.9545 

7.6625 
8.8923 
10.1591 

7.7794 
9.0517 
10.3685 

7.8983 
9.2142 
10.5828 

8.0192 
9.3800 
10.8021 

8.1420 
9.5491 
11.0266 

8.3938 
9.8975 
11.4913 

8.6540 
10.2598 
11.9780 

10 

11 
12 
13 

10.9497 

11.2034 

11.4639 

11.7314 

12.0061 

12.2882 

12.5779 

13.1808 

13.8164 

12.1687 
13.4121 
14.6803 

12.4835 
13.7956 
15.1404 

12.8078 
14.1920 
15.6178 

13.1420 
14.6020 
16.1130 

13.4864 
15.0258 
16.6268 

13.8412 
15.4640 
17.1599 

14.2068 
15.9171 
17.7130 

14.9716 
16.8699 

18.8821 

15.7836 
17.8885 
20.1406 

14 
15 
16 

15.9739 
17.2934 
18.6393 

16.5190 
17.9319 
19.3802 

17.0863 
18.5989 
20.1569 

17.6770 
19.2957 
20.9710 

18.2919 
20.0236 
21.8245 

18.9321 
20.7841 
22.7193 

19.5986 
21.5786 
23.6575 

21.0151 
23.2760 
25.6725 

22.5505 
25.1290 

27.8881 

17 
18 
19 

20.0121 
21.4123 
22.8406 

20.8647 
22.3863 
23.9460 

21.7616 
23.4144 
25.1169 

22.7050 
24.4997 
26.3572 

23.6975 
25.6454 
27.6712 

24.7417 
26.8551 
29.0636 

25.8404 
28.1324 
30.5390 

28.2129 
30.9057 
33.7600 

30.8402 
33.9990 
37.3790 

20 

21 
22 
23 

24.2974 

25.5447 

26.8704 

28.2797 

29.7781 

31.3714 

33.0660 

36.7856 

40.9955 

25.7833 
27.2990 
28.8450 

27.1833 
28.8629 
30.5844 

28.6765 
30.5368 
32.4529 

30.2695 
32.3289 
34.4604 

31.9692 
34.2480 
36.6179 

33.7831 
36.3034 
38.9370 

35.7193 
38.5052 
41.4305 

39.9927 
43.3923 
46.9958 

44.8652 
49.0057 
53.4361 

24 
25 
26 

30.4219 
32.0303 
33.6709 

32.3490 
34.1578 
36.0117 

34.4265 
36.4593 
38.5530 

36.6665 
38.9499 
41.3131 

39.0826 
41.6459 
44.3117 

41.6892 
44.5652 
47.5706 

44.5020 
47.7271 
51.1135 

50.8156 
54.8645 
59.1564 

58.1767 
63.2490 
68.6765 

27 
28 
29 

35.3443 
37.0512 
38.7922 

37.9120 
39.8598 
41.8563 

40.7096 
42.9309 
45.2189 

43.7591 
46.2906 
48.9108 

47.0842 
49.9676 
52.9663 

50.7113 
53.9933 
57.4230 

54.6691 
58.4026 
62.3227 

63.7058 
68.5281 
73.6398 

74.4838 
80.6977 
87.3465 

30 

31 

32 
33 

40.5681 

43.9027 

47.5754 

51.6227 

56.0849 

61.0071 

66.4388 

79.0582 

94.4608 

42.3794 
44.2270 
46.1116 

46.0003 
48.1503 
50.3540 

50.0027 
52.5028 
55.0778 

54.4295 
57.3345 
60.3412 

59.3283 
62.7015 
66.2095 

64.7524 
68.6662 
72.7562 

70.7608 
75.2988 
80.0638 

84.8017 
90.8898 
97.3432 

102.0730 
110.2182 
118.9334 

34 
35 

36 

48.0338 
49.9945 
51.9944 

52.6129 
54.9282 
57.3014 

57.7302 
60.4621 
63.2759 

63.4532 
66.6740 
70.0076 

69.8579 
73.6522 
77.5983 

77.0303 
81.4966 
86.1640 

85.0670 
90.3203 
95.8363 

104.1838 
111.4348 
119.1209 

128.2588 
138.2369 
148.9135 

37 
38 
39 

54.0343 
56.1149 
58.2372 

59.7339 
62.2273 
64.7830 

66.1742 
69.1594 
72.2342 

73.4579 
77.0289 
80.7249 

81.7022 
85.9703 
90.4091 

91.0413 
96.1382 
101.4644 

101.6281 
107.7095 
114.0950 

127.2681 
135.9042 
145.0585 

160.3374 
172.5610 
185.6403 

40 

60.4020 

67.4026 

75.4013 

84.5503 

95.0255 

107.0303 

120.7998 

154.7620 

199.6351 

41 
42 
43 

62.6100 
64.8622 
67.1595 

70.0876 
72.8398 
75.6608 

78.6633 
82.0232 
85.4839 

88.5095 
92.6074 
96.8486 

99.8265 
104.8196 
110.0124 

112.8467 
118.9248 
125.2764 

127.8398 
135.2318 
142.9933 

165.0477 
175.9505 
187.5076 

214.6096 
230.6322 
247.7765 

44 
45 
46 

69.5027 
71.8927 
74.3306 

78.5523 
81.5161 
84.5540 

89.0484 
92.7199 
96.5015 

101.2383 
105.7817 
110.4840 

115.4129 
121.0294 
126.8706 

131.9138 
138.8500 
146.0982 

151.1430 
159.7002 
168.6852 

199.7580 
212.7435 
226.5081 

266.1209 
285.7493 
306.7518 

47 
48 
49 

76.8172 
79.3535 
81.9400 

87.6679 
90.8596 
94.1311 

100.3965 
104.4084 
108.5406 

115.3510 
120.3883 
125.6018 

132.9454 
139.2632 
145.8337 

153.6726 
161.5879 
169.8594 

178.1194 
188.0254 
198.4267 

241.0986 
256.5645 
272.9584 

329.2244 
353.2701 
378.9990 

50 

84.5794 

97.4843 

112.7969 

130.9979 

152.6671 

178.5030 

209.3480 

290.3359 

406.5289 

XII  d]        Table  XII  d  —  Present  Value  of  an  Annuity 


131 


PRESENT  VALUE  OP  ONE  DOLLAR  PER  YEAR  FOR  n  YEARS 


n 

2% 

2k  % 

3% 

**% 

4% 

4\% 

5% 

6% 

7% 

I 
2 
3 

.9804 
1.9416 
2.8839 

.9756 
1.9274 
2.8560 

.9709 
1.9135 

2.8286 

.9662 
1.8997 
2.8016 

.9615 
1.8861 
2.7751 

.9569 
1.8727 
2.7490 

.9524 
1.8594 
2.7232 

.9434 
1.8334 
2.6730 

.9346 
1.8080 
2.6243 

4 
5 
6 

3.8077 
4.7135 
5.6014 

3.7620 
4.6458 
5.5081 

3.7171 
4.5797 
5.4172 

3.6731 
4.5151 
5.3286 

3.6299 
4.4518 
5.2421 

3.5875 
4.3900 
5.1579 

3.5460 
4.3295 
5.0757 

3.4651 
4.2124 
4.9173 

3.3872 
4.1002 
4.7665 

7 
8 
9 

6.4720 
7.3255 
8.1622 

6.3494 
7.1701 
7.9709 

6.2303 
7.0197 
7.7861 

6.1145 
6.8740 
7.6077 

6.0021 
6.7327 
7.4353 

5.8927 
6.5959 
7.2688 

5.7864 
6.4632 
7.1078 

5.5824 
6.2098 
6.8017 

5.3893 
5.9713 
6.5152 

10 

8.9826 

8.7521 

8.5302 

8.3166 

8.1109 

7.9127 

7.7217 

7.3601 

7.0236 

11 
12 
13 

9.7868 
10.5753 
11.3484 

9.5142 
10.2578 
10.9832 

9.2526 
9.9540 
10.6350 

9.0016 
9.6633 
10.3027 

8.7605 
9.3851 
9.9856 

8.5289 
9.1186 
9.6829 

8.3064 
8.8633 
9.3936 

7.8869 
8.3838 
8.8527 

7.4987 
7.9427 
8.3577 

14 
15 
16 

12.1062 
12.8493 
13.5777 

11.6909 
12.3814 
13.0550 

11.2961 
11.9379 
12.5611 

10.9205 
11.5174 
12.0941 

10.5631 
11.1184 
11.6523 

10.2228 
10.7395 
11.2340 

9.8986 
10.3797 
10.8378 

9.2950 
9.7122 
10.1059 

8.7455 
9.1079 
9.4466 

17 

18 
19 

14.2919 
14.9920 
15.6785 

13.7122 
14.3534 
14.9789 

13.1661 
13.7535 
14.3238 

12.6513 
13.1897 
13.7098 

12.1657 
12.6593 
13.1339 

11.7072 
12.1600 
12.5933 

11.2741 
11.6896 
12.0853 

10.4773 
10.8276 
11.1581 

9.7632 
10.0591 
10.3356 

20 

16.3514 

15.5892 

14.8775 

14.2124 

13.5903 

13.0079 

12.4622 

11.4699 

10.5940 

21 
22 
23 

17.0112 
17.6580 
18.2922 

16.1845 
16.7654 
17.3321 

15.4150 
15.9369 
16.4436 

14.6980 
15.1671 
15.6204 

14.0292 
14.4511 
14.8568 

13.4047 
13.7844 
14.1478 

12.8212 
13.1630 

13.4886 

11.7641 
12.0416 
12.3034 

10.8355 
11.0612 
11.2722 

24 
25 
26 

18.9139 
19.5235 
20.1210 

17.8850 
18.4244 
18.9506 

16.9355 
17.4131 
17.8768 

16.0584 
16.4815 
16.8904 

15.2470 
15.6221 
15.9828 

14.4955 
14.8282 
15.1466 

13.7986 
14.0939 
14.3752 

12.5504 
12.7834 
13.0032 

11.4693 
11.6536 
11.8258 

27 
28 
29 

20.7069 
21.2813 
21.8444 

19.4640 
19.9649 
20.4535 

18.3270 
18.7641 
19.1885 

17.2854 
17.6670 
18.0358 

16.3296 
16.6631 
16.9837 

15.4513 

15.7429 
16.0219 

14.6430 
14.8981 
15.1411 

13.2105 
13.4062 
13.5907 

11.9867 
12.1371 

12.2777 

30 

22.3965 

20.9303 

19.6004 

18.3920 

17.2920 

16.2889 

15.3725 

13.7648 

12.4090 

31 
32 
33 

22.9377 
23.4683 
23.9886 

21.3954 
21.8492 
22.2919 

20.0004 
20.3888 
20.7658 

18.7363 
19.0689 
19.3902 

17.5885 
17.8736 
18.1476 

16.5444 
16.7889 
17.0229 

15.5928 
15.8027 
16.0025 

13.9291 
14.0840 
14.2302 

12.5318 
12.6466 
12.7538 

34 
35 
36 

24.4986 
24.9986 

25.4888 

22.7238 
23.1452 
23.5563 

21.1318 
21.4872 
21.8323 

19.7007 
20.0007 
20.2905 

18.4112 
18.6646 
18.9083 

17.2468 
17.4610 
17.6660 

16.1929 
16.3742 
16.5469 

14.3681 
14.4982 
14.6210 

12.8540 
12.9477 
13.0352 

37 
38 
39 

25.9695 
26.4406 
26.9026 

23.9573 
24.3486 
24.7303 

22.1672 
22.4925 
22.8082 

20.5705 
20.8411 
21.1025 

19.1426 
19.3679 
19.5845 

17.8622 
18.0500 
18.2297 

16.7113 
16.8679 
17.0170 

14.7368 
14.8460 
14.9491 

13.1170 
13.1935 
13.2649 

40 

27.3555 

25.1028 

23.1148 

21.3551 

19.7928 

18.4016 

17.1591 

15.0463 

13.3317 

41 
42 
43 

27.7995 
28.2348 
28.6616 

25.4661 
25.8206 
26.1664 

23.4124 
23.7014 
23.9819 

21.5991 
21.8349 
22.0627 

19.9931 
20.1856 
20.3708 

18.5661 
18.7236 

18.8742 

17.2944 
17.4232 
17.5459 

15.1380 
15.2245 
15.3062 

13.3941 
13.4524 
13.5070 

44 
45 
46 

29.0800 
29.4902 
29.8923 

26.5038 
26.8330 
27.1542 

24.2543 
24.5187 
24.7754 

22.2828 
22.4955 
22.7009 

20.5488 
20.7200 
20.8847 

19.0184 
19.1563 

19.2884 

17.6628 
17.7741 
17.8801 

15.3832 
15.4558 
15.5244 

13.5579 
13.6055 
13.6500 

47 
48 
49 

30.2866 
30.6731 
31.0521 

27.4675 
27.7732 
28.0714 

25.0247 
25.2667 
25.5017 

22.8994 
23.0912 
23.2766 

21.0429 
21.1951 
21.3415 

19.4147 
19.5356 
19.6513 

17.9810 
18.0772 
18.1687 

15.5890 
15.6500 
15.7076 

13.6910 
13.7305 
13.7668 

50 

31.4236 

28.3623 

25.7298 

23.4556 

21.4822 

19.7620 

18.2559 

15.7619 

13.8007 

132    Table  XII  e  —  Logarithms  for  Interest  Computations   [XII  e 


r 

1  +  r 

log  (1  +  r) 

\% 

1.005 

00216  60617  56508 

1  % 

1.010 

00432  13737  82643 

14% 

1.015 

00646  60422  49232 

2% 

1.020 

008600171761918 

24% 

1.025 

01072  38653  91773 

3% 

1.030 

01283  72247  05172 

34% 

1.035 

01494  03497  92937 

4% 

1.040 

01703  33392  98780 

4=  % 

1.045 

019116290447073 

5% 

1.050 

021189299069938 

r 

1  +  r 

log  (1  +  r) 

54% 

1.055 

023252459633711 

6% 

1.060 

02530  58652  64770 

6*% 

1.065 

02734  96077  74757 

7% 

'  1.070 

02938  37776  85210 

1\% 

1.075 

03140  84642  51624 

8% 

1.080 

03342  37554  86950 

84% 

1.085 

03542  97381  84548 

9% 

1.090 

03742  64979  40624 

94% 

1.095 

03941  41191  76137 

10% 

1.100 

04139  26851  58225 

For  Amount,  A,  of  any  principal,  P,  after  n  years:  A  =  P(l  +  r)n. 
For  present  worth,  P,  of  any  amount,  A,  at  the  end  of  n  years:  P  =  A  -f-  (1  +  r)n. 
To  find  logarithms  and  antilogarithms  of  A  and  P  to  many  significant  figures,  use 
Table  XI,  p.  126,  and  Table  I  a,  p.  20. 


Table  XII  f — American  Experience  Mortality  Table 

Based  on  100,000  living  at  age  10 


At 
Age 

Number 

Surviving 

Deaths 

At 
Age 

Number 
Surviving 

Deaths 

At 
Age 

Number 
Surviving 

Deaths 

At 
Age 

Number 
Surviving 

Deaths 

10 

100,000 

749 

35 

81,822 

732 

60 

57,917 

1,546 

85 

5,485 

1,292 

11 

99,251 

746 

36 

81,090 

737 

61 

56,371 

1,628 

86 

4,193 

1,114 

12 

98,505 

743 

37 

80,353 

742 

62 

54,743 

1,713 

87 

3,079 

933 

13 

97,762 

740 

38 

79,611 

749 

63 

53,030 

1,800 

88 

2,146 

744 

14 

97,022 

737 

39 

78,862 

756 

64 

51,230 

1,889 

89 

1,402 

555 

15 

96,285 

735 

40 

78,106 

765 

65 

49,341 

1,980 

90 

847 

385 

16 

95,550 

732 

41 

77,341 

774 

66 

47,361 

2,070 

91 

462 

246 

17 

94,818 

729 

42 

76,567 

785 

67 

45,291 

2,158 

92 

216 

137 

18 

94,089 

727 

43 

75,782 

797 

68 

43,133 

2,243 

93 

79 

58 

19 

93,362 

725 

44 

74,985 

812 

69 

40,890 

2,321 

94 

21 

18 

20 

92,637 

723 

45 

74,173 

828 

70 

38,569 

2,391 

95 

3 

3 

21 

91,914 

722 

46 

73,345 

848 

71 

36,178 

2,448 

22 

91,192 

721 

47 

72,497 

870 

72 

33,730 

2,487 

23 

90,471 

720 

48 

71,627 

896 

73 

31,243 

2,505 

24 

89,751 

719 

49 

70,731 

927 

74 

28,738 

2,501 

25 

89,032 

718 

50 

69,804 

962 

75 

26,237 

2,476 

26 

88,314 

718 

51 

68,842 

1,001 

76 

23,761 

2,431 

27 

87,596 

718 

52 

67,841 

1,044 

77 

21,330 

2,369 

28 

86,878 

718 

53 

66,797 

1,091 

78 

18,961 

2,291 

29 

86,160 

719 

54 

65,706 

1,143 

79 

16,670 

2,196 

30 

85,441 

720 

55 

64,563 

1,199 

80 

14,474 

2,091 

31 

84,721 

721 

56 

63,364 

1,260 

81 

12,383 

1,964 

32 

84,000 

723 

57 

62,104 

1,325 

82 

10,419 

1,816 

33 

83,277 

726 

58 

60,779 

1,394 

83 

8,603 

1,648 

34 

82,551 

729 

59 

59,385 

1,468 

84 

6,955 

1,470 

XIII] 


Table  XIII  —  Important  Constants 


133 


LOGARITHMS  OF  IMPORTANT  CONSTANTS 


71  =  NUMBEB 

YALCB  or  n 

Loo  10  n 

7T 

3.14159265 

0.49714987 

1  -5-ir 

0.31830989 

9.50285013 

T» 

9.86960440 

0.99429975 

VT 

1.77245385 

0.24857494 

e  =  Naperian  Base 

2.71828183 

0.43429448 

M  =  logio  e 

0.43429448 

9.63778431 

1  -J-  M  =  log,  10 

2.30258509 

0.36221569 

180  -5-  IT  =  degrees  in  1  radian 

57.2957795 

1.75812263 

•JT  -5-  180  =  radians  in  1° 

0.01745329 

8.24187737 

TT  4-  10800  =  radians  in  1' 

0.0002908882 

6.46372612 

IT  -T-  648000  =  radians  in  1" 

0.000004848136811095 

4.68557487 

sin  1" 

0.00000484813681  1076 

4.68557487 

tan  1'^ 

0.00000484813681  1  133 

4.68557487 

centimeters  in  1  ft. 

30.480 

1.4840158 

feet  in  1  cm. 

0.032808 

8.5159842 

inches  in  1  m. 

39.37  (exact  legal  value) 

1.5951654 

pounds  in  1  kg. 

2.20462 

0.3433340 

kilograms  in  1  Ib. 

0.453593 

9.6566660 

g  (average  value) 

32.16  ft./sec./sec. 

1.5073 

=  981  cm./sec./sec. 

2.9916690 

weight  of  1  cu.  ft.  of  water 

62.425  Ib.  (max.  density) 

1.7953586 

weight  of  1  cu.  ft.  of  air 

0.0807  Ib.  (at  32°  F.) 

8.907 

cu.  in.  in  1  (U.  S.)  gallon 

231  (exact  legal  value) 

2.3636120 

ft.  Ib.  per  sec.  in  1  H.  P. 

550  (exact  legal  value) 

2.7403627 

kg.  m.  per  sec.  in  1  H.  P. 

76.0404 

1.8810445 

watts  in  1  H.  P. 

745.957 

2.8727135 

SEVERAL  NUMBERS  VERT  ACCURATELY 


IT  =  3.14159  26535  89793  23846  26433  83280 

e  =  2.71828  18284  59045  23536  02874  71353 

M  =  0.43429  44819  03251  82765  11289  18917 

1  -5-  M  =  2.30258  50929  94045  68401  79914  54684 

Iog10  TT  =  0.49714  98726  94133  85435  12682  88291 

logw  M  =  9.63778  43113  00536  78912 


CERTAIN  CONVENIENT  VALUES  FOR  n  =  1  TO  n  =  10 


n 

l/n 

V5 

# 

n! 

l/n! 

Looion 

1 

1.000000 

1.00000 

1.00000 

1 

1.0000000 

0.000000000 

2 

0.500000 

1.41421 

1.25992 

2 

0.5000000 

0.301029996 

3 

0.333333 

1.73205 

1.44225 

6 

0.1666667 

0.477121255 

4 

0.250000 

2.00000 

1.58740 

24 

0.0416667 

0.602059991 

5 

0.200000 

2.23607 

1.70998 

120 

0.0083333 

0.698970004 

6 

0.166667 

2.44949 

1.81712 

720 

0.0013889 

0.778151250 

7 

0.142857 

2.64575 

1.91293 

5040 

0.0001984 

0.845098040 

8 

0.125000 

2.82843 

2.00000 

40320 

0.0000248 

0.903089987 

9 

0.111111 

3.00000 

2.0S008 

362880 

0.0000028 

0.954242509 

10 

0.100000 

3.16228 

2.15443 

3628800 

0.0000003 

1.000000000 

134 


Table  XIV  a  —  Four  Place  Logarithms  pay  a 


N 

10 

11 
12 
13 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

123 

456 

789 

0000 

0043 

0086 

0128 

0170 

0212 

0253 

0294 

0334 

0374 

4  812 

172125 

29  33  37 

0414 
0792 
1139 

0453 
0828 
1173 

0492 
0864 
1206 

0531 
0899 
1239 

0569 
0934 
1271 

0607 
0969 
1303 

0645 
1004 
1335 

0682 
1038 
1367 

0719 
1072 
1399 

0755 
1106 
1430 

4  811 
3  710 
3  610 

15  1923 
141721 
131619 

26  30  34 
242831 
23  26  29 

14 
15 

16 

1461 
1761 
2041 

1492 
1790 
2068 

1523 
1818 
2095 

1553 
1847 
2122 

1584 
1875 
2148 

1614 
1903 
2175 

1644 
1931 
2201 

1673 
1959 

2227 

1703 
1987 
2253 

1732 
2014 
2279 

369 
368 
358 

121518 
11  1417 
111316 

21  24  27 
20  22  25 
18  21  24 

17 
18 
19 

20 

21 

22 
23 

2304 
2553 

2788 

2330 
2577 
2810 

2355 
2601 
2833 

2380 
2625 
2856 

2405 

2648 

2878 

2430 
2672 
2900 

2455 
2695 
2923 

2480 
2718 
2945 

2504 

2742 
2967 

2529 
2765 
2989 

257 
257 
247 

10  12  15 
91214 
91113 

17  20  22 
161921 
16  18  20 

3010 

3032 

3054 

3075 

3096 

3118 

3139 

3160 

3181 

3201 

246 

81113 

15  17  19 

3222 
3424 
3617 

3243 
3444 
3636 

3263 
3464 
3655 

3284 
3483 
3674 

3304 
3502 
3692 

3324 
3522 
3711 

3345 
3541 

3729 

3365 
3560 

3747 

3385 
3579 
3766 

3404 
3598 
3784 

246 
246 
246 

81012 
81012 
7    911 

14  16  18 
14  16  17 
13  15  17 

24 
25 
26 

3802 
3979 
4150 

3820 
3997 
4166 

3838 
4014 
4183 

3856 
4031 
4200 

3874 
4048 
4216 

3892 
4065 
4232 

3909 
4082 
4249 

3927 
4099 
4265 

3945 
4116 
4281 

3962 
4133 
4298 

245 
245 
235 

7    911 
7    910 
7    810 

12  14  16 
12  14  16 
11  1315 

27 
28 
29 

30 

4314 

4472 
4624 

4330 

4487 
4639 

4346 
4502 
4654 

4362 

4518 
4669 

4378 
4533 
4683 

4393 

4548 
4698 

4409 
4564 
4713 

4425 
4579 

4728 

4440 
4594 
4742 

4456 
4609 
4757 

235 

235 
134 

689 
689 

679 

11  12  14 
11  1214 
101213 

4771 

4786 

4800 

4814 

4829 

4843 

4857 

4871 

4886 

4900 

134 

679 

1011  13 

31 
32 
33 

4914 
5051 
5185 

4928 
5065 
5198 

4942 
5079 
5211 

4955 
5092 
5224 

4969 
5105 
5237 

4983 
5119 
5250 

4997 
5132 
5263 

5011 
5145 
5276 

5024 
5159 
5289 

5038 
5172 
5302 

134 
134 
134 

578 
578 
578 

1011  12 
9  11  12 
9ll  12 

34 
35 

36 

5315 
5441 
5563 

5328 
5453 
5575 

5340 
5465 
5587 

5353 

5478 
5599 

5366 
5490 
5611 

5378 
5502 
5623 

5391 
5514 
5635 

5403 
5527 
5647 

5416 
5539 
5658 

5428 
5551 
5670 

124 
124 
124 

568 
567 
567 

9  1011 
91011 
81011 

37 
38 
39 

5682 
5798 
5911 

5694 
5809 
5922 

57C5 
5821 
5933 

5717 
5832 
5944 

5729 

5843 
5955 

5740 
5855 
5966 

5752 
5866 
5977 

5763 

5877 
5988 

5775 
5888 
5999 

5786 
5899 
6010 

124 
123 
123 

567 
567 
457 

8    911 
8    910 
8    910 

40 

6021 

6031 

6042 

6053 

6064 

6075 

6085 

6096 

6107 

6117 

1  2  3 

456 

8    910 

41 
42 
43 

6128 
6232 
6335 

6138 
6243 
6345 

6149 
6253 
6355 

6160 
6263 
6365 

6170 
6274 
6375 

6180 
6284 
6385 

0191 
6294 
6395 

6201 
6304 
6405 

6212 
6314 
6415 

6222 
6325 
64?5 

123 
123 
123 

456 
456 
456 

789 
789 
789 

44 
45 
46 

6435 
6532 
6628 

6444 
6542 
6637 

6454 
6551 
6646 

6464 
6561 
6656 

6474 
6571 
6665 

6484 
6580 
6675 

6493 
6590 
6684 

6503 
6599 
6693 

6513 
6609 
6702 

6522 
6618 
6712 

123 
123 
123 

456 
456 
456 

789 
789 

778 

47 
48 
49 

50 

6721 
6812 
6902 

6730 
6821 
6911 

6739 
6830 
6920 

6749 
6839 
0928 

6758 
6848 
6937 

6767 
6857 
6946 

6776 
6866 
6955 

6785 
6875 
6964 

6794 

6884 
G972 

6803 
6893 
6981 

123 
123 
1  2  3 

456 
456 
445 

778 
778 
678 

6990 

6998 

7007 

7016 

7024 

7033 

7042 

7050 

7059 

7067 

123 

345 

678 

51 
52 
53 

7076 
7160 
7243 

7084 
7168 
7251 

7093 
7177 
7259 

7101 
7185 
7267 

7110 
7193 

7275 

7118 
7202 
7284 

7126 
7210 
7292 

7135 
7218 
7300 

7143 
7226 
7308 

7152 
7235 
7316 

123 
123 
122 

345 
345 
345 

678 
677 
667 

54 

7324 

7332 

7340 

7348 

7356 

7364 

7372 

7380 

7388 

7396 

122 

345 

667 

N 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

123 

456 

789 

The  proportional  parts  are  stated  in  full  for  every  tenth  at  the  right-hand  side. 
The  logarithm  of  any  number  of  four  significant  figures  can  be  read  directly  by  add- 


XIV  a]  Table  XIV  a  —  Four  Place  Logarithms 


135 


N 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

123 

456 

789 

55 

56 

57 
58 
59 

7404 
7482 

7559 
7634 
7709 

7412 
7490 

7566 
7642 
7716 

7419 
7497 

7574 
7649 
7723 

7427 
7505 

7582 
7657 
7731 

7435 
7513 

7589 
7664 

7738 

7443 
7520 

7597 
7672 

7745 

7451 

7528 

7604 
7679 
7752 

7459 
7536 

7612 
7686 
7760 

7466 
7543 

7619 
7694 

7767 

7474 
7551 

7627 
7701 

7774 

122 
122 

112 
112 
1  1  2 

345 
345 

345 

344 
344 

567 
567 

567 
567 
567 

60 

7782 

7789 

7796 

7803 

7810 

7818 

7825 

7832 

7839 

7840 

112 

344 

566 

61 
62 
63 

64 
65 
66 

67 
68 
69 

7853 
7924 
7993 

8062 
8129 
8195 

8261 
8325 

8388 

7860 
7931 
8000 

8069 
8136 
8202 

8267 
8331 

8395 

7868 
7938 
8007 

8075 
8142 
8209 

8274 
8338 
8401 

7875 
7945 
8014 

8082 
8149 
8215 

8280 
8344 
8407 

7882 
7952 
8021 

8089 
8156 
8222 

8287 
8351 
8414 

7889 
7959 
8028 

8096 
8162 
8228 

8293 
8357 
8420 

7896 
7966 
8035 

8102 
8169 
8235 

8299 
8363 
8426 

7903 
7973 
8041 

8109 
8176 
8241 

8306 
8370 
8432 

7910 
7980 
8048 

8116 
8182 
8248 

8312 
8376 
8439 

7917 
7987 
8055 

8122 
8189 
8254 

8319 

8382 
8445 

112 
112 
112 

112 
112 
112 

112 
112 
112 

334 
334 
334 

334 
334 
334 

334 
334 
334 

566 
556 
556 

556 
556 
556 

556 
456 
456 

70 

8451 

8457 

8463 

8470 

8476 

8482 

8488 

8494 

8500 

8506 

1  1  2 

334 

456 

71 
72 
73 

74 
75 
76 

77 
78 
79 

8513 
8573 
8633 

8692 
8751 
8808 

8865 
8921 
8976 

8519 
8579 
8639 

8698 
8756 
8814 

8871 
8927 
8982 

8525 
8585 
8645 

8704 
8762 
8820 

8876 
8932 
8987 

8531 
8591 
8651 

8710 
8768 
8825 

8882 
8938 
8993 

8537 
8597 
8657 

8716 

8774 
8831 

8887 
8943 
8998 

8543 
8603 
8663 

8722 
8779 
8837 

8893 
8949 
9004 

8549 
8609 
8669 

8727 
8785 
8842 

8899 
8954 
9009 

8555 
8615 
8675 

8733 
8791 
8848 

8904 
8960 
9015 

8561 
8621 
8681 

8739 
8797 
8854 

8910 
8965 
9020 

8567 
8627 
8686 

8745 
8802 
8859 

8915 
8971 
9025 

112 
112 
112 

112 

112 
112 

112 
112 
112 

334 
334 
234 

234 
233 
233 

233 
233 
233 

456 
456 
455 

455 
455 
445 

445 
445 

445 

80 

9031 

9036 

9042 

9047 

9053 

9058 

9063 

9069 

9074 

9079 

112 

233 

445 

81 
82 
83 

84 
85 

86 

87 
88 
89 

9085 
9138 
9191 

9243 
9294 
9345 

9395 
9445 
9494 

9090 
9143 
9196 

9248 
9299 
9350 

9400 
9450 
9499 

9096 
9149 
9201 

9253 
9304 
9355 

9405 
9455 
9504 

9101 
9154 
9206 

9258 
9309 
9360 

9410 
9460 
9509 

9106 
9159 
9212 

9263 
9315 
9365 

9415 
9465 
9513 

9112 
9165 
9217 

9269 
9320 
9370 

9420 
9469 
9518 

9117 
9170 
9222 

9274 
9325 
9375 

9425 
9474 
9523 

9122 
9175 
9227 

9279 
9330 
9380 

9430 
9479 
9528 

9128 
9180 
9232 

9284 
9335 
9385 

9435 
9484 
9533 

9133 
9186 
9238 

9289 
9340 
9390 

9440 
9489 
9538 

112 
112 
112 

112 

112 
112 

112 
Oil 
Oil 

233 
233 
233 

233 
233 
233 

233 
223 
223 

445 
445 
445 

445 

445 
445 

445 
344 

344 

90 

9542 

9547 

9552 

9557 

9562 

9566 

9571 

9576 

9581 

9580 

Oil 

223 

344 

91 
92 
93 

94 
95 
96 

97 
98 
99 

9590 
9638 
9685 

9731 
9777 
9823 

9868 
9912 
9956 

9595 
9643 
9689 

9736 
9782 
9827 

9872 
9917 
9961 

9600 
9647 
9694 

9741 
9786 
9832 

9877 
9921 
9965 

9605 
9652 
9699 

9745 
9791 
9836 

9881 
9926 
9969 

9609 
9657 
9703 

9750 
9795 
9841 

9886 
9930 
9974 

9614 
9661 
9708 

9754 
9800 
9845 

9890 
9934 
9978 

9619 
9666 
9713 

9759 
9805 
9850 

9894 
9939 
9983 

9624 
9671 
9717 

9763 

9809 
9854 

9899 
9943 

9987 

9628 
9675 
9722 

9768 
9814 
9859 

9903 
9948 
9991 

9633 
9680 
9727 

9773 
9818 
9863 

9908 
9952 
9996 

Oil 
0  1  1 
Oil 

Oil 
0  1  1 
Oil 

Oil 

Oil 
Oil 

223 
223 
223 

223 
223 
223 

223 
223 
223 

344 
344 
344 

344 

344 
344 

344 
334 
334 

N 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

123 

456 

789 

ing  the  proportional  part  corresponding  to  the  fourth  figure  to  the  tabular  number 
corresponding  to  the  first  three  figures.     There  may  be  an  error  of  1  in  the  last  place. 


136          Table  XIV  b  —  Antifogarithms  to  Four  Places     [XIV  b 


0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

123 

456 

789 

.00 

1000 

1002 

1005 

1007 

1009 

1012 

1014 

1016 

1019 

1021 

001 

111 

222 

.01 
.02 
.03 

1023 
1047 
1072 

1026 
1050 
1074 

1028 
1052 
1076 

1030 
1054 
1079 

1033 
1057 
1081 

1035 
1059 
1084 

1038 
1062 
1086 

1040 
1064 
1089 

1042 
1067 
1091 

1045 
1069 
1094 

001 
001 
0  0  1 

1  1  1 
111 
111 

222 
222 
222 

.04 
.05 

.06 

1096 
1122 
1148 

1099 
1125 
1151 

1102 
1127 
1153 

1104 
1130 
1156 

1107 
1132 
1159 

1109 
1135 
1161 

1112 
1138 
1164 

1114 
1140 
1167 

1117 
1143 
1169 

1119 
1146 
1172 

0  1  1 
0  1  1 
Oil 

112 
1  1  2 
112 

222 

222 
222 

.07 
.08 
.09 

1175 
1202 
1230 

1178 
1205 
1233 

1180 
1208 
1236 

1183 
1211 
1239 

1186 
1213 

1242 

1189 
1216 
1245 

1191 
1219 

1247 

1194 
1222 
1250 

1197 
1225 
1253 

1199 
1227 
1256 

Oil 
0  1  1 
0  1  1 

112 
112 
112 

222 
223 
223 

.10 

1259 

1262 

1265 

1268 

1271 

1274 

1276 

1279 

1282 

1285 

Oil 

112 

223 

.11 
.12 
.13 

1288 
1318 
1349 

1291 
1321 
1352 

1294 
1324 
1355 

1297 
1327 
1358 

1300 
1330 
1361 

1303 
1334 
1365 

1306 
1337 
1368 

1309 
1340 
1371 

1312 
1343 
1374 

1315 
1346 
1377 

Oil 
Oil 
Oil 

1  2  2 
122 
122 

223 
223 
233 

.14 
.15 
.16 

1380 
1413 
1445 

1384 
1416 
1449 

1387 
1419 
1452 

1390 
1422 
1455 

1393 
1426 
1459 

1396 
1429 
1462 

1400 
1432 
1466 

1403 
1435 
1469 

1406 
1439 

1472 

1409 
1442 
1476 

Oil 
Oil 
Oil 

122 

122 
122 

233 
233 
233 

.17 

.18 
.19 

1479 
1514 
1549 

1483 
1517 
1552 

1486 
1521 
1556 

1489 
1524 
1560 

1493 
1528 
1563 

1496 
1531 
1567 

1500 
1535 
1570 

1503 
1538 
1574 

1507 
1542 
1578 

1510 
1545 
1581 

Oil 
Oil 
Oil 

122 
122 
122 

233 

233 
233 

.20 

1585 

1589 

1592 

1596 

1600 

1603 

1607 

1611 

1614 

1618 

Oil 

122 

333 

.21 
.22 
.23 

1622 
1660 
1698 

1626 
1663 
1702 

1629 
1667 
1706 

1633 
1671 
1710 

1637 
1675 
1714 

1641 
1679 
1718 

1644 
1683 
1722 

1648 
1687 
1726 

1652 
1690 
1730 

1656 
1694 
1734 

Oil 
Oil 
Oil 

122 
222 
222 

333 
333 
333 

.24 
.25 

.26 

1738 
1778 
1820 

1742 
1782 
1824 

1746 
1786 
1828 

1750 
1791 
1832 

1754 
1795 
1837 

1758 
1799 
1841 

1762 
1803 
1845 

1766 
1807 
1849 

1770 
1811 
1854 

1774 
1816 
1858 

Oil 
Oil 
0  1  1 

222 
223 
223 

334 
334 
334 

.27 

.28 
.29 

1862 
1905 
1950 

1866 
1910 
1954 

1871 
1914 
1959 

1875 
1919 
1963 

1879 
1923 
1968 

1884 
1928 
1972 

1888 
1932 
1977 

1892 
1936 
1982 

1897 
1941 
1986 

1901 
1945 
1991 

Oil 
Oil 
Oil 

223 
223 
223 

334 

344 
344 

.30 

1995 

2000 

2004 

2009 

2014 

2018 

2023 

2028 

2032 

2037 

Oil 

223 

344 

.31 
.32 
.33 

2042 
2089 
2138 

2046 
2094 
2143 

2051 
2099 
2148 

2056 
2104 
2153 

2061 
2109 
2158 

2065 
2113 
2163 

2070 
2118 
2168 

2075 
2123 
2173 

2080 
2128 
2178 

2084 
2133 
2183 

0  1  1 
0  1  1 
Oil 

223 
223 
223 

344 
344 
344 

.34 
.35 

.36 

2188 
2239 
2291 

2193 

2244 
2296 

2198 
2249 
2301 

2203 
2254 
2307 

2208 
2259 
2312 

2213 
2265 
2317 

2218 
2270 
2323 

2223 
2275 
2328 

2228 
2280 
2333 

2234 
2286 
2339 

112 

112 
112 

233 
233 
233 

445 
445 
445 

.37 
.38 
.39 

2344 
2399 
2455 

2350 
2404 
2460 

2355 
2410 
2466 

2360 

2415 
2472 

2366 
2421 

2477 

2371 

2427 
2483 

2377 
2432 
2489 

2382 

2438 
2495 

2388 
2443 
2500 

2393 
2449 
2506 

112 

112 
1  1  2 

233 
233 
233 

445 
455 
455 

.40 

2512 

2518 

2523 

2529 

2535 

2541 

2547 

2553 

2559 

2564 

1  1  2 

234 

455 

.41 
.42 
.43 

2570 
2630 
2692 

2576 
2636 
2698 

2582 
2642 
2704 

2588 
2649 
2710 

2594 
2655 
2716 

2600 
2661 
2723 

2606 
2667 
2729 

2612 
2673 
2735 

2618 
2679 
2742 

2624 
2685 
2748 

1  1  2 
112 
1  1  2 

234 
234 
234 

456 
456 
456 

.44 
.45 
.46 

2754 

2818 
2884 

2761 
2825 
2891 

2767 
2831 
2897 

2773 
2838 
2904 

2780 
2844 
2911 

2786 
2851 
2917 

2793 

2858 
2924 

2799 
2864 
2931 

2805 
2871 
2938 

2812 

2877 
2944 

112 
112 
112 

334 
334 
334 

456 
556 
556 

.47 
.48 
.49 

2951 
3020 
3090 

2958 
3027 
3097 

2965 
3034 
3105 

2972 
3041 
3112 

2979 
3048 
3119 

2985 
3055 
3126 

2992 
3062 
3133 

2999 
3069 
3141 

3006 
3076 
3148 

3013 
3083 
3155 

112 
112 
112 

334 

334 
344 

566 
566 
566 

XIV  b]     Table  XIV  b  —  Antilogarithms  to  Four  Places 


137 


0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

123 

456 

789 

.50 

31G2 

3170 

3177 

3184 

3192 

3199 

3200 

3214 

3221 

322b 

112 

344 

567 

.51 
.52 
.53 

3236 
3311 
3388 

3243 
3319 
3396 

3251 
3327 
3404 

3258 
3334 
3412 

3266 
3342 
3420 

3273 
3350 
3428 

3281 
3357 
3436 

3289 
3365 
3443 

3296 
3373 
3451 

3304 
3381 
3459 

112 
112 
122 

344 
345 

345 

567 
567 
667 

.54 
.55 

.56 

3467 
3548 
3631 

3475 
3556 
3639 

3483 
3565 
3648 

3491 
3573 
3656 

3499 
3581 
3664 

3508 
3589 
3673 

3516 
3597 
3681 

3524 
3606 
3690 

3532 
3614 
3698 

3540 
3622 
3707 

122 

122 
122 

345 
345 
345 

667 

677 
678 

.57 

.58 
.59 

3715 
3802 
3890 

3724 
3811 

3899 

3733 
3819 
3908 

3741 
3828 
3917 

3750 
3837 
3926 

3758 
3846 
3936 

3767 
3855 
3945 

3776 
3864 
3954 

3784 
3873 
3963 

3793 

3882 
3972 

123 
123 

123 

345 
345 
455 

678 
678 

678 

.60 

3981 

3990 

3999 

4009 

4018 

4027 

4036 

4046 

4055 

4064 

123 

456 

788 

.61 
.62 
.63 

4074 
4169 
4266 

4083 
4178 
4276 

4093 
4188 
4285 

4102 
4198 
4295 

4111 
4207 
4305 

4121 
4217 
4315 

4130 
4227 
4325 

4140 
4236 
4335 

4150 
4246 
4345 

4159 
4256 
4355 

123 
123 
123 

456 
456 
456 

789 
789 
789 

.64 
.65 

.66 

4365 
4467 
4571 

4375 
4477 
4581 

4385 

4487 
4592 

4395 
4498 
4603 

4406 
4508 
4613 

4416 
4519 
4624 

4426 
4529 
4634 

4436 
4539 
4645 

4446 
4550 
4656 

4457 
4560 
4667 

123 
123 
123 

456 
456 
456 

789 
789 
7    910 

.67 
.68 
.69 

4677 

4786 
4898 

4688 
4797 
4909 

4699 

4808 
4920 

4710 
4819 
4932 

4721 
4831 
4943 

4732 

4842 
4955 

4742 
4853 
4966 

4753 
4864 

4977 

4764 

4875 
4989 

4775 
4887 
5000 

123 
123 
123 

457 
567 
567 

8   910 

8    9  10 
8    9  10 

.70 

5012 

5023 

5035 

5047 

5058 

5070 

5082 

5093 

5105 

5117 

123 

567 

8    910 

.71 
.72 

.73 

5129 
5248 
5370 

5140 
5260 
5383 

5152 
5272 
5395 

5164 
5284 
5408 

5176 
5297 
5420 

51SS 
5309 
5433 

5200 
5321 
5445 

5212 
5333 
5458 

5224 
5346 
5470 

5236 
5358 
5483 

124 
124 
1  3  4 

567 
567 
567 

81011 
91011 
91011 

.74 
.75 

.76 

5495 
5623 
5754 

5508 
5636 
5768 

5521 
5649 
5781 

5534 
5662 
5794 

5546 
5675 

5808 

5559 
5689 
5821 

5572 
5702 
5834 

5585 
5715 

5848 

5598 
5728 
5861 

5610 
5741 
5875 

134 
1  3  4 
134 

568 
578 
578 

9  1012 
911  12 
911  12 

.77 
.78 
.79 

5888 
6026 
6166 

5902 
6039 
6180 

5916 
6053 
6194 

5929 
6067 

6209 

5943 

6081 
6223 

5957 
6095 
6237 

5970 
6109 
6252 

5984 
6124 
6266 

5998 
6138 

6281 

6012 
6152 

6295 

134 
134 
134 

578 
678 
679 

101112 
1011  13 
1011  13 

.80 

6310 

6324 

6339 

G353 

6368 

6383 

6397 

G412 

6427 

6442 

134 

679 

10  12  13 

.81 
.82 

.83 

>457 
6607 
6761 

6471 
6622 
6776 

6486 
6637 
6792 

6501 
6653 
6808 

6516 
6668 
6823 

6531 
6683 
6839 

6546 
6699 
6855 

6561 
6714 
6871 

6577 
6730 
6887 

6592 
6745 
6902 

235 
235 
235 

689 
689 
689 

11  1214 
11  1214 
11  13  14 

.84 
.85 

.86 

6918 
7079 
7244 

6934 
7096 
7261 

6950 
7112 

7278 

6966 
7129 
7295 

6982 
7145 
7311 

6998 
7161 

7328 

7015 
7178 
7345 

7031 
7194 
7362 

7047 
7211 
7379 

7063 

7228 
7396 

235 
235 
235 

7  810 
7  810 
7  810 

11  13  15 

12  13  15 
12  14  15 

.87 
.88 
.89 

7413 

7586 
7762 

7430 
7603 
7780 

7447 
7621 

7798 

7464 

7638 

7816 

7482 
7656 
7834 

7499 
7674 

7852 

7516 
7691 

7870 

7534 
7709 

-SS9 

7551 

7727 
7907 

7568 

7745 
"925 

245 

245 
246 

7  910 
7911 
7  911 

12  14  16 
12  14  16 
13  15  16 

.90 

7943 

7962 

7980 

7998 

8017 

8035 

8054 

8072 

8091 

8110 

246 

7  911 

13  15  17 

.91 
.92 
.93 

8128 
8318 
8511 

8147 
8337 
8531 

8166 
8356 
8551 

8185 
8375 
8570 

8204 
8395 
8590 

8222 
8414 
8610 

8241 
8433 
8630 

8260 
8453 
8650 

8279 
8472 
8670 

8299 
8492 
8690 

246 
246 
246 

8911 
81012 
81012 

13  15  17 
14  15  17 
14  16  18 

.94 
.95 

.96 

8710 
8913 
9120 

8730 
8933 
9141 

8750 
8954 
9162 

8770 
8974 
9183 

8790 
8995 
9204 

8810 
9016 
9226 

8831 
9036 
9247 

8851 
9057 
9268 

8872 
9078 
9290 

8892 
9099 
9311 

246 
246 
246 

81012 
81012 
9  11  13 

14  16  18 
15  17  19 
15  17  19 

.97 
.98 
.99 

9333 
9550 
9772 

9354 

9572 
9795 

9376 
9594 
9817 

9397 
9616 

9840 

9419 
9638 

9863 

9441 
9661 

0886 

9462 
9683 
9908 

9484 
9705 
9931 

9506 
9727 
9954 

9528 

9750 
9977 

246 
247 
257 

91113 
911  13 
9  11  14 

15  17  19 

16  18  20 
161821 

138    Table  XIV  c  —  Four  Place  Trigonometric  Functions  [XIV  c 

[Characteristics  of  Logarithms  omitted — determine  by  the  usual  rule  from  the  value] 


SINE 

TANGENT 

COTANGENT 

COSINE 

IADIANS 

DEGREES 

Value  Logw 

Value  Logio 

Value   Logio 

Value   Logio 

oono 

0°OO' 

noon  - 

noon  - 

i  nfion  onoo 

90°  00' 

1  ^708 

•  \J\S\J\J 

.0029 

W 

10 

0029  .4637 

•\j\j\j\j 
.0029  .4637 

343.77  .5363 

\.*\j\j\j\j  f\j\j\j\j 
1.0000  .0000 

vVf   \J\J 

50 

i  .•  >  i  \j<j 
1.5679 

.0058 

20 

0058  .7648 

.0058  .7648 

171.89  .2352 

1.0000  .0000 

40 

1.5650 

.0087 

30 

0087  .9408 

.0087  .9409 

114.59  .0591 

1.0000  .0000 

30 

1.5621 

.0116 

40 

0116  .0658 

.0116  .0658 

85.940  .9342 

.9999  .0000 

20 

1.5592 

.0145 

50 

0145  .1627 

.0145  .1627 

68.750  .8373 

.9999  .0000 

10 

1.5563 

.0175 

1°00' 

0175  .2419 

.0175  .2419 

57.290  .7581 

.9998  .9999 

89°  00' 

1.5533 

.0204 

10 

0204  .3088 

.0204  .3089 

49.104  .6911 

.9998  .9999 

50 

1.5504 

.0233 

20 

0233  .3668 

.0233  .3669 

42.964  .6331 

.9997  .9999 

40 

1.5475 

.0262 

30 

0262  .4179 

.0262  .4181 

38.188  .5819 

.9997  .9999 

30 

1.5446 

.0291 

40 

0291  .4637 

.0291  .4638 

34.368  .5362 

.9996  .9998 

20 

1.5417 

.0320 

50 

0320  .5050 

.0320  .5053 

31.242  .4947 

.9995  .9998 

10 

1.5388 

.0349 

2°  00' 

0349  .5428 

.0349  .5431 

28.636  .4569 

.9994  .9997 

88°  00' 

1.5359 

.0378 

10 

0378  .5776 

.0378  .5779 

26.432  .4221 

.9993  .9997 

50 

1.5330 

.0407 

20 

0407  .6097 

.0407  .6101 

24.542  .3899 

.9992  .9996 

40 

1.5301 

.0436 

30 

0436  .6397 

.0437  .6401 

22.904  .3599 

.9990  .9996 

30 

1.5272 

.0465 

40 

0465  .6677 

.0466  .6682 

21.470  .3318 

.9989  .9995 

20 

1.5243 

.0495 

50 

0494  .6940 

.0495  .6945 

20.206  .3055 

.9988  .9995 

10 

1.5213 

.0524 

3°  00' 

0523  .7188 

.0524  .7194 

19.081  .2806 

.9986  .9994 

87°  00' 

1.5184 

.0553 

10 

0552  .7423 

.0553  .7429 

18.075  .2571 

.9985  .9993 

50 

1.5155 

.0582 

20 

0581  .7645 

.0582  .7652 

17.169  .2348 

.9983  .9993 

40 

1.5126 

.0611 

30 

0610  .7857 

.0612  .7865 

16.350  .2135 

.9981  .9992 

30 

1.5097 

.0640 

40 

0640  .8059 

.0641  .8067 

15.605  .1933 

.9980  .9991 

20 

1.5068 

.0669 

50 

0669  .8251 

.0670  .8261 

14.924  .1739 

.9978  .9990 

10 

1.5039 

.0698 

4°  00' 

0698  .8436 

.0699  .8446 

14.301  .1554 

.9976  .9989 

86°  00' 

1.5010 

.0727 

10 

0727  .8613 

.0729  .8624 

13.727  .1376 

.9974  .9989 

50 

1.4981 

.0756 

20 

0756  .8783 

.0758  .8795 

13.197  .1205 

.9971  .9988 

40 

1.4952 

.0785 

30 

0785  .8946 

.0787  .8960 

12.706  .1040 

.9969  .9987 

30 

1.4923 

.0814 

40 

.0814  .9104 

.0816  .9118 

12.251  .0882 

.9967  .9986 

20 

1.4893 

.0844 

50 

.0843  .9256 

.0846  .9272 

11.826  .0728 

.9964  .9985 

10 

1.4864 

.0873 

5°  00' 

.0872  .9403 

.0875  .9420 

11.430  .0580 

.9962  .9983 

85°  00' 

1.4835 

.0902 

10 

0901  .9545 

.0904  .9563 

11.059  .0437 

.9959  .9982 

50 

1.4806 

.0931 

20 

.0929  .9682 

.0934  .9701 

10.712  .0299 

.9957  .9981 

40 

1.4777 

.0960 

30 

.0958  .9816 

.0963  .9836 

10.385  .0164 

.9954  .9980 

30 

1.4748 

.0989 

40 

.0987  .9945 

.0992  .9966 

10.078  .0034 

.9951  .9979 

20 

1.4719 

.1018 

50 

.1016  .0070 

.1022  .0093 

9.7882  .9907 

.9948  .9977 

10 

1.4690 

.1047 

6°  00' 

.1045  .0192 

.1051  .0216 

9.5144  .9784 

.9945  .9976 

84°  00' 

1.4661 

.1076 

10 

.1074  .0311 

.1080  .0336 

9.2553  .9664 

.9942  .9975 

50 

1.4632 

.1105 

20 

.1103  .0426 

.1110  .0453 

9.0098  .9547 

.9939  .9973 

40 

1.4603 

.1134 

30 

.1132  .0539 

.1139  .0567 

8.7769  .9433 

.9936  .9972 

30 

1.4573 

.1164 

40 

.1161  .0648 

.1169  .0678 

8.5555  .9322 

.9932  .9971 

20 

1.4544 

.1193 

50 

.1190  .0755 

.1198  .0786 

8.3450  .9214 

.9929  .9969 

10 

1.4515 

.1222 

7°  00' 

.1219  .0859 

.1228  .0891 

8.1443  .9109 

.9925  .9968 

83°  00' 

1.4486 

.1251 

10 

.1248  .0961 

.1257  .0995 

7.9530  .9005 

.9922  .9966 

50 

1.4457 

.1280 

20 

.1276  .1060 

.1287  .1096 

7.7704  .8904 

.9918  .9964 

40 

1.4428 

.1309 

30 

.1305  .1157 

.1317  .1194 

7.5958  .8806 

.9914  .9963 

30 

1.4399 

.1338 

40 

.1334  .1252 

.1346  .1291 

7.4287  .8709 

.9911  .9961 

20 

1.4370 

.1367 

50 

.1363  .1345 

.1376  .1385 

7.2687  .8615 

.9907  .9959 

10 

1.4341 

.1396 

8°  00' 

.1392  .1436 

.1405  .1478 

7.1154  .8522 

.9903  .9958 

82°  00' 

1.4312 

.1425 

10 

.1421  .1525 

.1435  .1569 

6.9682  .8431 

.9899  .9956 

50 

1.4283 

.1454 

20 

.1449  .1612 

.1465  .1658 

6.8269  .8342 

.9894  .9954 

40 

1.4254 

.1484 

30 

.1478  .1697 

.1495  .1745 

6.6912  .8255 

.9890  .9952 

30 

1.4224 

.1513 

40 

.1507  .1781 

.1524  .1831 

6.5606  .8169 

.9886  .9950 

20 

1.4195 

.1542 

50 

.1536  .1863 

.1554  .1915 

6.4348  .8085 

.9881  .9948 

10 

1.4166 

.1571 

9°  00 

.1564  .1943 

.1584  .1997 

6.3138  .8003 

.9877  .9946 

81°  00' 

1.4137 

Value  Logio 
COSINE 

Value  Logio 
COTANGENT 

Value   Logio 
TANGENT 

Value   Logio 

SINE 

DEGREES 

RADIANS 

XIV  c]  Four  Place  Trigonometric  Functions  139 

[Characteristics  of  Logarithms  omitted — determine  by  the  usual  rule  from  the  value] 


SINE 

TANGENT 

COTANGENT 

COSINE 

\ADIAN5 

.DEGREES 

Value  Logic 

Value  Logic 

Value   Logic 

Value  Logic 

.1571 

9°  00' 

.1564  .1943 

.1584  .1997 

6.3138  .8003 

.9877  .9946 

81°  00' 

1.4137 

.1000 

10 

.1593  .2022 

.1614  .2078 

6.1970  .7922 

.9872  .9944 

50 

1.4108 

.1629 

20 

.1622  .2100 

.1644  .2158 

6.0844  .7842 

.9868  .9942 

40 

1.4079 

.1658 

30 

.1650  .2176 

.1673  .2236 

5.9758  .7764 

.9863  .9940 

30 

1.4050 

.1687 

40 

.1679  .2251 

.1703  .2313 

5.8708  .7687 

.9858  .9938 

20 

1.4021 

.1716 

50 

.1708  .2324 

.1733  .2389 

5.7694  .7611 

.9853  .9936 

10 

1.3992 

.1745 

10°  00' 

.1736  .2397 

.1763  .2463 

5.6713  .7537 

.9848  .9934 

80°  00' 

1.3963 

.1774 

10 

.1765  .2468 

.1793  .2536 

5.5764  .7464 

.9843  .9931 

50 

1.3934 

.1804 

20 

.1794  .2538 

.1823  .2609 

5.4845  .7391 

.9838  .9929 

40 

1.3904 

.1833 

30 

.1822  .2606 

.1853  .2680 

5.3955  .7320 

.9833  .9927 

30 

1.3875 

.1862 

40 

.1851  .2674 

.1883  .2750 

5.3093  .7250 

.9827  .9924 

20 

1.3846 

.1891 

50 

.1880  .2740 

.1914  .2819 

5.2257  .7181 

.9822  .9922 

10 

1.3817 

.1920 

11°  00' 

.1908  .2806 

.1944  .2887 

5.1446  .7113 

.9816  .9919 

79°  00' 

1.3788 

.1949 

10 

.1937  .2870 

.1974  .2953 

5.0658  .7047 

.9811  .9917 

50 

1.3759 

.1978 

20 

.1965  .2934 

.2004  .3020 

4.9894  .6980 

.9805  .9914 

40 

1.3730 

.2007 

30 

.1994  .2997 

.2035  .3085 

4.9152  .6915 

.9799  .9912 

30 

1.3701 

.2036 

40 

.2022  .3058 

.2065  .3149 

4.8430  .6851 

.9793  .9909 

20 

1.3672 

.2065 

50 

.2051  .3119 

.2095  .3212 

4.7729  .6788 

.9787  .9907 

10 

1.3643 

.2094 

12°  cxy 

.2079  .3179 

.2126  .3275 

4.7046  .6725 

.9781  .9904 

78°  00' 

1.3614 

.2123 

10 

.2108  .3238 

.2156  .3336 

4.6382  .6664 

.9775  .9901 

50 

1.3584 

.2153 

20 

.2136  .3296 

.2186  .3397 

4.5736  .6603 

.9769  .9899 

40 

1.3555 

.2182 

30 

.2164  .3353 

.2217  .3458 

4.5107  .6542 

.9763  .9896 

30 

1.3526 

.2211 

40 

.2193  .3410 

.2247  .3517 

4.4494  .6483 

.9757  .9893 

20 

1.3497 

.2240 

50 

.2221  .3466 

.2278  .3576 

4.3897  .6424 

.9750  .9890 

10 

1.3468 

.2269 

13°  OO7 

.2250  .3521 

.2309  .3634 

4.3315  .6366 

.9744  .9887 

77°  00' 

1.3439 

.2298 

10 

.2278  .3575 

.2339  ,3691 

4.2747  .6309 

.9737  .9884 

50 

1.3410 

.2327 

20 

.2306  .3629 

.2370  .3748 

4.2193  .6252 

.9730  .9881 

40 

1.3381 

.2356 

30 

.2334  .3682 

.2401  .3804 

4.1653  .6196 

.9724  .9878 

30 

1.3352 

.2385 

40 

.2363  .3734 

.2432  .3859 

4.1126  .6141 

.9717  .9875 

20 

1.3323 

.2414 

50 

.2391  .3786 

.2462  .3914 

4.0611  .6086 

.9710  .9872 

10 

1.3294 

.2443 

14°  (XX 

.2419  .3837 

.2493  .3968 

4.0108  .6032 

.9703  .9869 

76°  (Xy 

1.3265 

.2473 

10 

.2447  .3887 

.2524  .4021 

3.9617  .5979 

.9696  .9866 

50 

1.3235 

.2502 

20 

.2476  .3937 

.2555  .4074 

3.9136  .5926 

.9689  .9863 

40 

1.3206 

.2531 

30 

.2504  .3986 

.2586  .4127 

3.8667  .5873 

.9681  .9859 

30 

1.3177 

.2560 

40 

.2532  .4035 

.2617  .4178 

3.8208  .5822 

.9674  .9856 

20 

1.3148 

.2589 

50 

.2560  .4083 

.2648  .4230 

3.7760  .5770 

.9667  .9853 

10 

1.3119 

.2618 

15°  00' 

.2588  .4130 

.2679  .4281 

3.7321  .5719 

.9659  .9849 

75°  00' 

1.3090 

.2647 

10 

.2616  .4177 

.2711  .4331 

3.6891  .5669 

.9652  .9846 

50 

1.3061 

.2676 

20 

.2644  .4223 

.2742  .4381 

3.6470  .5619 

.9644  .9843 

40 

1.3032 

.2705 

30 

.2672  .4269 

.2773  .4430 

3.6059  .5570 

.9636  .9839 

30 

1.3003 

.2734 

40 

.2700  .4314 

.2805  .4479 

3.5656  .5521 

.9628  .9836 

20 

1.2974 

.2763 

50 

.2728  .4359 

.2836  .4527 

3.5261  .5473 

.9621  .9832 

10 

1.2945 

.2793 

16°  00' 

.2756  .4403 

.2867  .4575 

3.4874  .5425 

.9613  .9828 

74°  00' 

1.2915 

.2822 

10 

.2784  .4447 

.2899  .4622 

3.4495  .5378 

.9605  .9825 

50 

1.2886 

.2851 

20 

.2812  .4491 

.2931  .4669 

3.4124  .5331 

.9596  .9821 

40 

1.2857 

.2880 

30 

.2840  .4533 

.2962  .4716 

3.3759  .5284 

.9588  .9817 

30 

1.2828 

.2909 

40 

.2868  .4576 

.2994  .4762 

3.3402  .5238 

.9580  .9814 

20 

1.2799 

.2938 

50 

.2896  .4618 

.3026  .4808 

3.3052  .5192 

.9572  .9810 

10 

1.2770 

.2967 

17°  00' 

.2924  .4659 

.3057  .4853 

3.2709  .5147 

.9563  .9806 

73°  00' 

1.2741 

.2996 

10 

.2952  .4700 

.3089  .4898 

3.2371  .5102 

.9555  .9802 

50 

1.2712 

.3025 

20 

.2979  .4741 

.3121  .4943 

3.2041  .5057 

.9546  .9798 

40 

1.2683 

.3054 

30 

.3007  .4781 

.3153  .4987 

3.1716  .5013 

.9537  .9794 

30 

1.2654 

.3083 

40 

.3035  .4821 

.3185  .5031 

3.1397  .4969 

.6528  .9790 

20 

1.2625 

.3113 

50 

.3062  .4861 

.3217  .5075 

3.1084  .4925 

.9520  .9786 

10 

1.2595 

.3142 

18°  00' 

.3090  .4900 

.3249  .5118 

3.0777  .4882 

.9511  .9782 

72°  00' 

1.2566 

Value  Logic 
COSINE 

Value  Logic 
COTANGENT 

Value   Logic 
TANGENT 

Value  Logic 
Bum 

DEGREES 

RADIANS 

140  Four  Place  Trigonometric  Functions 

[Characteristics  of  Logarithms  omitted — determine  by  the  usual  rule  from  the  value] 


[XIV  c 


RADIANS 

DEGREES 

SINE 
Value  Logio 

TANGENT 
Value  Logio 

COTANGENT 
Value   Logio 

COBINH 
Value  Logio 

.3142 

18°  00' 

.3090  .4900 

.3249  .5118 

3.0777  .4882 

.9511  .9782 

72°  00' 

1.2566 

.3171 

10 

.3118  .4939 

.3281  .5161 

3.0475  .4839 

.9502  .9778 

50 

1.2537 

.3200 

20 

.3145  .4977 

.3314  .5203 

3.0178  .4797 

.9492  .9774 

40 

1.2508 

.3229 

30 

.3173  .5015 

.3346  .5245 

2.9887  .4755 

.9483  .9770 

30 

1.2479 

.3258 

40 

.3201  .5052 

.3378  .5287 

2.9600  .4713 

.9474  .9765 

20 

1.2450 

.3287 

50 

.3228  .5090 

.3411  .5329 

2.9319  .4671 

.9465  .9761 

10 

1.2421 

.3316 

19°  00' 

.3256  .5126 

.3443  .5370 

2.9042  .4630 

.9455  .9757 

71°  00' 

1.2392 

.3345 

10 

.3283  .5163 

.3476  .5411 

2.8770  .4589 

.9446  .9752 

50 

1.2363 

.3374 

20 

.3311  .5199 

.3508  .5451 

2.8502  .4549 

.9436  .9748 

40 

1.2334 

.3403 

30 

.3338  .5235 

.3541  .5491 

2.8239  .4509 

.9426  .9743 

30 

1.2305 

.3432 

40 

.3365  .5270 

.3574  .5531 

2.7980  .4469 

.9417  .9739 

20 

1.2275 

.3462 

50 

.3393  .5306 

.3607  .5571 

2.7725  .4429 

.9407  .9734 

10 

1.2246 

.3491 

20°  00' 

.3420  .5341 

.3640  .5611 

2.7475  .4389 

.9397  .9730 

70°  00' 

1.2217 

.3520 

10 

.3448  .5375 

.3673  .5650 

2.7228  .4350 

.9387  .9725 

50 

1.2188 

.3549 

20 

.3475  .5409 

.3706  .5689 

2.6985  .4311 

.9377  .9721 

40 

1.2159 

.3578 

30 

.3502  .5443 

.3739  .5727 

2.6746  .4273 

.9367  .9716 

30 

1.2130 

.3607 

40 

.3529  .5477 

.3772  .5766 

2.6511  .4234 

.9356  .9711 

20 

1.2101 

.3636 

50 

.3557  .5510 

.3805  .5804 

2.6279  .4196 

.9346  .9706 

10 

1.2072 

.3665 

21°  00' 

.3584  .5543 

.3839  .5842 

2.6051  .4158 

.9336  .9702 

69°  00' 

1.2043 

.3694 

10 

.3611  .5576 

.3872  .5879 

2.5826  .4121 

.9325  .9697 

50 

1.2014 

.3723 

20 

.3638  .5609 

.3906  .5917 

2.5605  .4083 

.9315  .9692 

40 

1.1985 

.3752 

30 

.3665  .5641 

.3939  .5954 

2.5386  .4046 

.9304  .9687 

30 

1.1956 

.3782 

40 

.3692  .5673 

.3973  .5991 

2.5172  .4009 

.9293  .9682 

20 

1.1926 

.3811 

50 

.3719  .5704 

.4006  .6028 

2.4960  .3972 

.9283  .9677 

10 

1.1897 

.3840 

22°  00' 

.3746  .5736 

.4040  .6064 

2.4751  .3936 

.9272  .9672 

68°  00' 

1.1868 

.3869 

10 

.3773  .5767 

.4074  .6100 

2.4545  .3900 

.9261  .9667 

60 

1.1839 

.3898 

20 

.3800  .5798 

.4108  .6136 

2.4342  .3864 

.9250  .9661 

40 

1.1810 

.3927 

30 

.3827  .5828 

.4142  .6172 

2.4142  .3828 

.9239  .9656 

30 

1.1781 

.3956 

40 

.3854  .5859 

.4176  .6208 

2.3945  .3792 

.9228  .9651 

20 

1.1752 

.3985 

50 

.3881  .5889 

.4210  .6243 

2.3750  .3757 

.9216  .9646 

10 

1.1723 

.4014 

23°  00' 

.3907  .5919 

.4245  .6279 

2.3559  .3721 

.9205  .9640 

67°  00' 

1.1694 

.4043 

10 

.3934  .5948 

.4279  .6314 

2.3369  .3686 

.9194  .9635 

50 

1.1665 

.4072 

20 

.3961  .5978 

.4314  .6348 

2.3183  .3652 

.9182  .9629 

40 

1.1636 

.4102 

30 

.3987  .6007 

.4348  .6383 

2.2998  .3617 

.9171  .9624 

30 

1.1606 

.4131 

40 

.4014  .6036 

.4383  .6417 

2.2817  .3583 

.9159  .9618 

20 

1.1577 

.4160 

50 

.4041  .6065 

.4417  .6452 

2.2637  .3548 

.9147  .9613 

10 

1.1548 

.4189 

24°  00' 

.4067  .6093 

.4452  .6486 

2.2460  .3514 

.9135  .9607 

66°  00' 

1.1519 

.4218 

10 

.4094  .6121 

.4487  .6520 

2.2286  .3480 

.9124  .9602 

50 

1.1490 

.4247 

20 

.4120  .6149 

.4522  .6553 

2.2113  .3447 

.9112  .9596 

40 

1.1461 

.4276 

30 

.4147  .6177 

.4557  .6587 

2.1943  .3413 

.9100  .9590 

30 

1.1432 

.4305 

40 

.4173  .6205 

.4592  .6620 

2.1775  .3380 

.9088  .9584 

20 

1.1403 

.4334 

50 

.4200  .6232 

.4628  .6654 

2.1609  .3346 

.9075  .9579 

10 

1.1374 

.4363 

25°  00' 

.4226  .6259 

.4663  .6687 

2.1445  .3313 

.9063  .9573 

65°  00' 

1.1345 

.4392 

10 

.4253  .6286 

.4699  .6720 

2.1283  .3280 

.9051  .9567 

60 

1.1316 

.4422 

20 

.4279  .6313 

.4734  .6752 

2.1123  .3248 

.9038  .9561 

40 

1.1286 

.4451 

30 

.4305  .6340 

.4770  .6785 

2.0965  .3215 

.9026  .9555 

30 

1.1257 

.4480 

40 

.4331  .6366 

.4806  .6817 

2.0809  .3183 

.9013  .9549 

20 

1.1228 

.4509 

50 

.4358  .6392 

.4841  .6850 

2.0655  .3150 

.9001  .9543 

10 

1.1199 

.4538 

26°  00' 

.4384  .6418 

.4877  .6882 

2.0503  .3118 

.8988  .9537 

64°  00' 

1.1170 

.4567 

10 

.4410  .6444 

.4913  .6914 

2.0353  .3086 

.8975  .9530 

50 

1.1141 

.4596 

20 

.4436  .6470 

.4950  .6946 

2.0204  .3054 

.8962  .9524 

40 

1.1112 

.4625 

30 

.4462  .6495 

.4986  .6977 

2.0057  .3023 

.8949  .9518 

30 

1.1083 

.4654 

40 

.4488  .6521 

.5022  .7009 

1.9912  .2991 

.8936  .9512 

20 

1.1054 

.4683 

50 

.4514  .6546 

.5059  .7040 

1.9768  .2960 

.8923  .9505 

10 

1.1025 

.4712 

27°  00' 

.4540  .6570 

.5095  .7072 

1.9626  .2928 

.8910  .9499 

63°  00' 

1.0996 

Value  Logio 

Value  Logio 

Value   Logio 

Value  Logio 

DEGREES 

1  \ADIAN8 

COSINE 

COTANGENT 

TANGENT 

SINE 

XIV  c]  Four  Place  Trigonometric  Functions  141 

[Characteristics  of  Logarithms  omitted — determine  by  the  usual  rule  from  the  value] 


RADIANS 

DEGREES 

Sure 
Value  Logio 

TANGENT 
Value  Logio 

COTANGENT 
Value   Logio 

COSINE 
Value  Logic 

.4712 

27°  00' 

.4540  .6570 

.5095  .7072 

1.9626  .2928 

.8910  .9499 

63°  00' 

1.0996 

.4741 

10 

.4566  .6595 

.5132  .7103 

1.9486  .2897 

.8897  .9492 

50 

1.0966 

.4771 

20 

.4592  .6620 

.5169  .7134 

1.9347  .2866 

.8884  .9486 

40 

1.0937 

.4800 

30 

.4617  .6644 

.5206  .7165 

1.9210  .2835 

.8870  .9479 

30 

1.0908 

.4829 

40 

.4643  .6668 

.5243  .7196 

1.9074  .2804 

.8857  .9473 

20 

1.0879 

.4858 

50 

.4669  .6692 

.5280  .7226 

1.8940  .2774 

.8843  .9466 

10 

1.0850 

.4887 

28°  00' 

.4695  .6716 

.5317  .7257 

1.8807  .2743 

.8829  .9459 

62°  00' 

1.0821 

.4916 

10 

.4720  .6740 

.5354  .7287 

1.8676  .2713 

.8816  .9453 

50 

1.0792 

.4945 

20 

.4746  .6763 

.5392  .7317 

1.8546  .2683 

.8802  .9446 

40 

1.0763 

.4974 

30 

.4772  .6787 

.5430  .7348 

1.8418  .2652 

.8788  .9439 

30 

1.0734 

.5003 

40 

.4797  .6810 

.5467  .7378 

1.8291  .2622 

.8774  .9432 

20 

1.0705 

.5032 

50 

.4823  .6833 

.5505  .7408 

1.8165  .2592 

.8760  .9425 

10 

1.0676 

.5061 

29°  00' 

.4848  .6856 

.5543  .7438 

1.8040  .2562 

.8746  .9418 

61°  OO7 

1.0647 

.5091 

10 

.4874  .6878 

.5581  .7467 

1.7917  .2533 

.8732  .9411 

50 

1.0617 

.5120 

20 

.4899  .6901 

.5619  .7497 

1.7796  .2503 

.8718  .9404 

40 

1.0588 

.5149 

30 

.4924  .6923 

.5658  .7526 

1.7675  .2474 

.8704  .9397 

30 

1.0559 

.5178 

40 

.4950  .6946 

.5696  .7556 

1.7556  .2444 

.8689  .9390 

20 

1.0530 

.5207 

50 

.4975  .6968 

.5735  .7585 

1.7437  .2415 

.8675  .9383 

10 

1.0501 

.5236 

30°  00' 

.5000  .6990 

.5774  .7614 

1.7321  .2386 

.8660  .9375 

60°  00' 

1.0472 

.5265 

10 

.5025  .7012 

.5812  .7644 

1.7205  .2356 

.8646  .9368 

50 

1.0443 

.5294 

20 

.5050  .7033 

.5851  .7673 

1.7090  .2327 

.8631  .9361 

40 

1.0414 

.5323 

30 

.5075  .7055 

.5890  .7701 

1.6977  .2299 

.8616  .9353 

30 

1.0385 

.5352 

40 

.5100  .7076 

.5930  .7730 

1.6864  .2270 

.8601  .9346 

20 

1.0356 

.5381 

50 

5125  .7097 

.5969  .7759 

1.6753  .2241 

.8587  .9338 

10 

1.0327 

.5411 

31°  00' 

.5150  .7118 

.6009  .7788 

1.6643  .2212 

.8572  .9331 

59°  00' 

1.0297 

.5440 

10 

5175  .7139 

.6048  .7816 

1.6534  .2184 

.8557  .9323 

50 

1.0268 

.5469 

20 

.5200  .7160 

.6088  .7845 

1.6426  .2155 

.8542  .9315 

40 

1.0239 

.5498 

30 

.5225  .7181 

.6128  .7873 

1.6319  .2127 

.8526  .9308 

30 

1.0210 

.5527 

40 

5250  .7201 

.6168  .7902 

1.6212  .2098 

.8511  .9300 

20 

1.0181 

.5556 

50 

5275  .7222 

.6208  .7930 

1.6107  .2070 

.8496  .9292 

10 

1.0152 

.5585 

32°  00' 

5299  .7242 

.6249  .7958 

1.6003  .2042 

.8480  .9284 

58°  00' 

1.0123 

.5614 

10 

5324  .7262 

.6289  .7986 

1.5900  .2014 

.8465  .9276 

50 

1.0094 

.5643 

20 

5348  .7282 

.6330  .8014 

1.5798  .1986 

.8450  .9268 

40 

1.0065 

.5672 

30 

5373  .7302 

.6371  .8042 

1.5697  .1958 

.8434  .9260 

30 

1.0036 

.5701 

40 

.5398  .7322 

.6412  .8070 

1.5597  .1930 

.8418  .9252 

20 

1.0007 

.5730 

50 

.5422  .7342 

.6453  .8097 

1.5497  .1903 

.8403  .9244 

10 

.9977 

.5760 

33°  00' 

.5446  .7361 

.6494  .8125 

1.5399  .1875 

.8387  .9236 

57°  00' 

.9948 

.5789 

10 

.5471  .7380 

.6536  .8153 

1.5301  .1847 

.8371  .9228 

50 

.9919 

.5818 

20 

5495  .7400 

.6577  .8180 

1.5204  .1820 

.8355  .9219 

40 

.9890 

.5847 

30 

.5519  .7419 

.6619  .8208 

1.5108  .1792 

.8339  .9211 

30 

.9861 

.5876 

40 

.5544  .7438 

.6661  .8235 

1.5013  .1765 

.8323  .9203 

20 

.9832 

.5905 

50 

5568  .7457 

.6703  .8263 

1.4919  .1737 

.8307  .9194 

10 

.9803 

.5934 

34°  00' 

.5592  .7476 

.6745  .8290 

1.4826  .1710 

.8290  .9186 

66°  00' 

.9774 

.5963 

10 

5616  .7494 

.6787  .8317 

1.4733  .1683 

.8274  .9177 

50 

.9745 

.5992 

20 

.5640  .7513 

.6830  .8344 

1.4641  .1656 

.8258  .9169 

40 

.9716 

.6021 

30 

.5664  .7531 

.6873  .8371 

1.4550  .1629 

.8241  .9160 

30 

.9687 

.6050 

40 

5688  .7550 

.6916  .8398 

1.4460  .1602 

.8225  .9151 

20 

.9657 

.6080 

50 

5712  .7568 

.6959  .8425 

1.4370  .1575 

.8208  .9142 

10 

.9628 

.6109 

35°  00' 

.5736  .7586 

.7002  .8452 

1.4281  .1548 

.8192  .9134 

55°  00' 

.9599 

.6138 

10 

.5760  .7604 

.7046  .8479 

1.4193  .1521 

.8175  .9125 

50 

.9570 

.6167 

20 

.5783  .7622 

.7089  .8506 

1.4106  .1494 

.8158  .9116 

40 

.9541 

.6196 

30 

.5807  .7640 

.7133  .8533 

1.4019  .1467 

.8141  .9107 

30 

.9512 

.6225 

40 

.5831  .7657 

.7177  .8559 

1.3934  .1441 

.8124  .9098 

20 

.9483 

.6254 

50 

.5854  .7675 

.7221  .8586 

1.3848  .1414 

.8107  .9089 

10 

.9454 

.6283 

36°  00' 

.5878  .7692 

.7265  .8613 

1.3764  .1387 

.8090  .9080 

54°  00' 

.9425 

Value  Logio 

Value  Logio 

Value   Logio 

Value  Logio 

COSINE 

COTANGENT 

TANGKNT 

SINE 

^ 

142  Four  Place  Trigonometric  Functions 

[Characteristics  of  Logarithms  omitted — determine  by  the  usual  rule  from  the  value] 


[XIV  c 


RADIANS 

DEGREES 

SINE 
Value  Logio 

TANGENT 
Value   Logio 

COTANGENT 
Value   Logio 

COSINE 
Value  Logio 

.6283 

36°  00' 

.5878  .7692 

.7265  .8613 

1.3764  .1387 

.8090  .9080 

54°  00' 

.9425 

.6312 

10 

.5901  .7710 

.7310  .8639 

1.3680  .1361 

.8073  .9070 

50 

.9396 

.6341 

20 

.5925  .7727 

.7355  .8666 

1.3597  .1334 

.8056  .9061 

40 

.9367 

.6370 

30 

.5948  .7744 

.7400  .8692 

1.3514  .1308 

.8039  .9052 

30 

.9338 

.6400 

40 

.5972  .7761 

.7445  .8718 

1.3432  .1282 

.8021  .9042 

20 

.9308 

.6429 

50 

.5995  .7778 

.7490  .8745 

1.3351  .1255 

.8004  .9033 

10 

.9279 

.6458 

37°  00' 

.6018  .7795 

.7536  .8771 

1.3270  .1229 

.7986  .9023 

53°  00' 

.9250 

.6487 

10 

.6041  .7811 

.7581  .8797 

1.3190  .1203 

.7969  .9014 

50 

.9221 

.6516 

20 

.6065  .7828 

.7627  .8824 

1.3111  .1176 

.7951  .9004 

40 

.9192 

.6545 

30 

.6088  .7844 

.7673  .8850 

1.3032  .1150 

.7934  .8995 

30 

.9163 

.6574 

40 

.6111  .7861 

.7720  .8876 

1.2954  .1124 

.7916  .8985 

20 

.9134 

.6603 

50 

.6134  .7877 

.7766  .8902 

1.2876  .1098 

.7898  .8975 

10 

.9105 

.6632 

38°  00' 

.6157  .7893 

.7813  .8928 

1.2799  .1072 

.7880  .8965 

52°  00' 

.9076 

.6661 

10 

.6180  .7910 

.7860  .8954 

1.2723  .1046 

.7862  .8955 

50 

.9047 

.6690 

20 

.6202  .7926 

.7907  .8980 

1.2647  .1020 

.7844  .8945 

40 

.9018 

.6720 

30 

.6225  .7941 

.7954  .9006 

1.2572  .0994 

.7826  .8935 

30 

.8988 

.6749 

40 

.6248  .7957 

.8002  .9032 

1.2497  .0968 

.7808  .8925 

20 

.8959 

.6778 

50 

.6271  .7973 

.8050  .9058 

1.2423  .0942 

.7790  .8915 

10 

.8930 

.6807 

39°  00' 

.6293  .7989 

.8098  .9084 

1.2349  .0916 

.7771  .8905 

51°  00' 

.8901 

.6836 

10 

.6316  .8004 

.8146  .9110 

1.2276  .0890 

.7753  .8895 

60 

.8872 

.6865 

20 

.6338  .8020 

.8195  .9135 

1.2203  .0865 

.7735  .8884 

40 

.8843 

.6894 

30 

.6361  .8035 

.8243  .9161 

1.2131  .0839 

.7716  .8874 

30 

.8814 

.6923 

40 

.6383  .8050 

.8292  .9187 

1.2059  .0813 

.7698  .8864 

20 

.8785 

.6952 

50 

.6406  .8066 

.8342  .9212 

1.1988  .0788 

.7679  .8853 

10 

.8756 

.6981 

40°  00' 

.6428  .8081 

.8391  .9238 

1.1918  .0762 

.7660  .8843 

50°  00' 

.8727 

.7010 

10 

.6450  .8096 

.8441  .9264 

1.1847  .0736 

.7642  .8832 

50 

.8698 

.7039 

20 

.6472  .8111 

.8491  .9289 

1.1778  .0711 

.7623  .8821 

40 

.8668 

.7069 

30 

.6494  .8125 

.8541  .9315 

1.1708  .0685 

.7604  .8810 

30 

.8639 

.7098 

40 

.6517  .8140 

.8591  .9341 

1.1640  .0659 

.7585  .8800 

20 

.8610 

.7127 

50 

.6539  .8155 

.8642  .9366 

1.1571  .0634 

.7566  .8789 

10 

.8581 

.7156 

41°  00' 

.6561  .8169 

.8693  .9392 

1.1504  .0608 

.7547  .8778 

49°  00 

.8552 

.7185 

10 

.6583  .8184 

.8744  .9417 

1.1436  .0583 

.7528  .8767 

50 

.8523 

.7214 

20 

.6604  .8198 

.8796  .9443 

1.1369  .0557 

.7509  .8756 

40 

.8494 

.7243 

30 

.6626  .8213 

.8847  .9468 

1.1303  .0532 

.7490  .8745 

30 

.8465 

.7272 

40 

.6648  .8227 

.8899  .9494 

1.1237  .0506 

.7470  .8733 

20 

.8436 

.7301 

50 

.6670  .8241 

.8952  .9519 

1.1171  .0481 

.7451  .8722 

10 

.8407 

.7330 

42°  00' 

.6691  .8255 

.9004  .9544 

1.1106  .0456 

.7431  .8711 

48°  00 

.8378 

.7359 

10 

.6713  .8269 

.9057  .9570 

1.1041  .0430 

.7412  .8699 

50 

.8348 

.7389 

20 

.6734  .8283 

.9110  .9595 

1.0977  .0405 

.7392  .8688 

40 

.8319 

.7418 

30 

.6756  .8297 

.9163  .9621 

1.0913  .0379 

.7373  .8676 

30 

.8290 

.7447 

40 

.6777  .8311 

.9217  .9646 

1.0850  .0354 

.7353  .8665 

20 

.8261 

.7476 

50 

.6799  .8324 

.9271  .9671 

1.0786  .0329 

.7333  .8653 

10 

.8232 

.7505 

43°  00' 

.6820  .8338 

.9325  .9697 

1.0724  .0303 

.7314  .8641 

47°  00 

.8203 

.7534 

10 

.6841  .8351 

.9380  .9722 

1.0061  .0278 

.7294  .8629 

50 

.8174 

.7563 

20 

.6862  .8365 

.9435  .9747 

1.0599  .0253 

.7274  .8618 

40 

.8145 

.7592 

30 

.6884  .8378 

.9490  .9772 

1.0538  .0228 

.7254  .8606 

30 

.8116 

.7621 

40 

.6905  .8391 

.9545  .9798 

1.0477  .0202 

.7234  .8594 

20 

.8087 

.7650 

50 

.6926  .8405 

.9601  .9823 

1.0416  .0177 

.7214  .8582 

10 

.8058 

.7679 

44°  00' 

.6947  .8418 

.9657  .9848 

1.0355  .0152 

.7193  .8569 

46°  00 

.8029 

.7709 

10 

.6967  .8431 

.9713  .9874 

1.0295  .0126 

.7173  .8557 

50 

.7999 

.7738 

20 

.6988  .8444 

.9770  .9899 

1.0235  .0101 

.7153  .8545 

40 

.7970 

.7767 

30 

.7009  .8457 

.9827  .9924 

1.0176  .0076 

.7133  .8532 

30 

.7941 

.7796 

40 

.7030  .8469 

.9884  .9949 

1.0117  .0051 

.7112  .8520 

20 

.7912 

.7825 

50 

.7050  .8482 

.9942  .9975 

1.0058  .0025 

.7092  .8507 

10 

.7883 

.7854 

45°  00' 

.7071  .8495 

1.0000  .0000 

1.0000  .0000 

.7071  .8495 

45°  00 

.7854 

Value  Logic 

COSINE 

Value   Logio 

COTANGENl 

Value   Logio 
TANGENT 

Value  Logio 
SINE 

DEGREES 

RADIANS 

SLIDE-RULE 


y 
•3 

J_ 

1 

I 
^ 

I 


(2)    (3) 


(4) 


DIRECTIONS 


A  reasonably  accurate  slide-rule 
may  be  made  by  the  student,  for 
temporary    practice,     as 
Take   three   strips   of   heavy   stiff 
cardboard   1".3  wide  by  6"  long; 
these  are  shown  in  cross-section  in 
(1),     (2),     (3)     above. 
paste    or   glue   the    adjoining   cut 
of  the  slide  rule.     Then 
(2)   and   (3)   accurately  along  the 
lines  marked.     Paste  o 
pieces   together   as   shown   in    (4) 
and     (5).     Then     (5)     forms 
slide  of  the  slide-rule,  and  it  will 
fit  in  the  groove  in  (4)  if  the  work 
has    been    carefully    done. 
off  the  ends  as  shown  in  the  large 
cut. 


< 

:    a 

Q 

O 

o 

1 

=  = 

llB/ 

=  = 

at 

CD  •  = 

o» 

II 

z  = 

II 

-  — 

Ixx       ' 



^  ^D 

=  = 

^ 

i  = 

n 

=  = 

E     ^ 

~  — 

—  — 

(5) 

ro  - 

=  = 

ro 

to  -  = 

=     -(O 

E    -in 

nrule 
:,  for 

CM   - 

-- 

CM 

-=r  •  S 

E    -^t 

lows. 

— 

— 

Stiff 

i 

— 

long; 

=  - 

=  = 

m  _ 

on  in 

—  — 

=  = 

(3) 

EE 

in 

cut 

\r>  - 

=  - 

in 

strips 

=  = 

=  = 

j  the 

EE 

5  the 

00  - 

-  = 

m 

i    (4) 

•4-V.^. 

-- 

tne 

-- 

N 

will 

=  = 

—  — 

—  — 

work 

— 

1%.;™ 

— 

inm 

— 

i 

— 

large 

— 

< 

C      I 

Q 

O 

a 

'•tf'i^-v-yt' 


